Not an expert-- still working on these issues myself-- but I think that with gypcrete below and engineered wood above, you could have pretty much any underlay you want without worrying. You are getting great efficiancy from the choices you've already made, and the underlay is such a [relatively] small part of the equation that it won't be a problem.

Since you have chosen warmboard over gypcrete, what was your reasoning behind it besides responsiveness? I am sorry for the confusion. I didn't build a house with Warmboard, I had it in a house where original owner had installed it. It wasn't a house I built. I used it in the sense that I heated the house with it. I looked at the Gypcrete system and somehow feels uneasy about it. Doing a concrete pour over first and second floor does not sound structurally sound to me. Gypcrete has positives and negatives but shouldn't be overlooked because of structurally sound. I think a competent and knowledgeable designer is much more important than which type of system you use. So if you don't have a lot of experienced local people, you have to find experienced people who can help design at a distance. I would start with Radiant Engineering (talk to many companies though). A long somewhat unbiased discussion of radiant: First, it should be noted that radiant heat isn't an efficiency discussion. As people have pointed out many times hydronic radiant systems rarely have a positive payback. They are simply too expensive to install and they never payback if you are installing central air. However, every decision in your house isn't about payback. There are many decisions, such as paint color, cabinet color, cabinet design, many fixtures, etc., that are about your enjoyment of your home. No one has a pool installed because they want it to add value to their house. Radiant fits soundly into that category. Next: A discussion of trade-offs between the different systems. It is important to note that ALL radiant floor systems will provide a comfortable environment to a home that other heating methods struggle to achieve. There are basically five considerations in radiant heat (1) installation costs, (2) operating costs, (3) responsiveness (4) allowable customization and (5) noise (as hot water passes through cold aluminum plates it makes noise). If we look at the different systems we can typically see how they handle each of these things. Warmboard is (1) very expensive to install, (2) it has a low operating cost as it is a warm water system rather than a hot water system, (3) incredibly responsive for radiant heat (able to heat a structure in hours rather than days), (4) low customization and (5) low noise. Underfloor transfer plate systems are (1) moderately expensive to install, (2) low operating costs as they are also warm rather than hot water systems, (3) are somewhat responsive (4) highly customizable and (5) have more expansion noise. Gypcrete overpour is (1) moderately expensive (still cheaper than the two above), (2) have low costs as,they too are warm water systems, (3) not responsive at all, (4) are highly customizable and (5) eliminate almost all noise. Staple up systems are (1) pretty cheap (2) high operating costs as they are a hot water system, (3) not responsive at all, (4) limited customization (they are more limited by physics than design), and (5) are pretty noisy. So looking at Warmboard vs. similar systems - the only real concern from using any aluminum covered plywood system is the noise. Warmboard eliminates expansion noise because of the "special" glue they use to adhere the aluminum to the wood. I can't really tell you how special their glue is, I feel confident they will say super special and their competition will disagree. Warmboard type systems vs. underfloor transfer plate systems - Warmboard is quieter but the loops are not really customizable. Loops are 8" apart with Warmboard, so you can choose not to put warmboard in places but you can't get the loops closer together. With transfer plate systems you can customize the heat of a room by simply moving the loops closer together. This means that you can make the floor right outside the shower warmer than the floor beside the toilet (not many people spend a lot of time standing beside their toilet), but there is more expansion noise. Warmboard is a bit more responsive than transfer plates. Warmboard vs, gypcrete overpour - Gypcrete overpour gives you almost unlimited customization without the noise associated with aluminum transfer plate systems. However, it is not at all responsive. Staple up systems - They are more expensive to operate than any of the above systems but are cheaper to install and easier to maintain. You are not likely to nail through a staple up system with a nice thick transfer plate. Also easier to remodel with staple up systems. TL:DR In the end, if I was ranking a radiant system today - I would probably rank it - underfloor transfer plates > gypcrete > Warmboard. But it is a three way photo finish so it wouldn't take a lot to change the order. Also noisy houses don't bother me at all.

Do you need ROOM heat or do you want "warm toes"? If you need to heat the entire house using in-floor radiant heat (I'm assuming you are going with hydronic?) then the best option is always concrete, tile or stone. They offer the least resistance which means the most amount of heat pours through them and into the house. If you want warm feet (because the rest of the house is being heated by a fully operational forced air or baseboard heat system) then you can have engineered hardwood as a lovely option. There are SOME engineered hardwood floors that allow it being used over hydronic in-floor radiant heat....but do NOT count on it being "OK" with every engineered product you look at. And if you go with hardwood, you do NOT want to used underlayment or soft underpad with the heating system. The underpad will block quite a bit of the heat, creating excess load on your heat system (in essence you are heating the pad under the floor while the room remains chilly). Carpet is an amazing product when used with in-floor radiant heat. Carpet breathes nicely. And the underpad is the thing that has to have the "hydronic heating" allowance which means you can choose the pad that is best suited for your situation. The other thing to be aware of with wood and in-floor radiant heat: low humidity. In-floor radiant heat is KNOWN to dry out wood flooring products. Because the wood is SOOOO close to the elements, the first thing that heats up (and dries out) is the wood. To combat this issue, you MUST add in humidity control in the home. That means you will need a system (separate from the heating system) that has the ability to add/subtract humidity throughout the year. In Montana the outdoor humidity is often very low to begin with. If you then decrease it even more with a dry heat, then the interior humidity levels can be extremely low. And wood does NOT like that. A wood floor requires humidity to "sit" around about 45% all year round. Please check your building specifications to find out HOW you are going to add that humidity to your home. And then find out if you have the ability to change the humidity levels with the touch of a button (humidistat). This usually involves a system with heating/cooling ducts so that moisture can be added to the air in an even way... For right now, I would assume you HAVE to go with tile/stone/concrete until you find out the HVAC humidity control system that is currently in place for your build.

From personal experience, not technical point, of view, I love LVP. We have hydronic radiant heat throughout (and three large dogs in a snowy climate). On the main floor and upper floor, our tubes are set in warmboard which I understand is more efficient than a staple up installation. The tile in the bathrooms is the warmest underfoot and the carpet in the bedrooms is the least warm underfoot. The LVP in the rest of the house is in between. All three heat about the same, but are in different zones so not an apples to oranges comparison. I keep the bedrooms cooler. LVP has been great with the dogs — no worries about water bowls and tracking in snow. I wet mop often. I love the look of tile, but after having it in the kitchen in my old house for more than 30 years, never again. I cook a lot and occasionally for several hours at a time and tile was really hard on my back. The difference is amazing. My back hurt so much more at 45 cooking in my old kitchen than it does now at 65 on a softer surface.