I understand your inspiration, what inlay are you actually wanting to use? The inlay in this picture looks like it is inset into the wood flooring . Almost like they routed (sp?) the item into the board after the boards were installed. If the inlay is set to go around the edges of the floor where walking is less likely to occur, I wonder if you can select a different style of inlay. Something that is not flat but is rounded maybe? that way the inlay can sit slightly above the wood and minimize some of the gaping. It is hard to make a judgment on this as we do not really know all the details. I am wondering if Schluter has a product that could offer a solution. Attached the Schluter catalog link below. Might be worth checking out. I do think that for what you want you are going to have to make some concessions. Do you want to pay the labor for someone to perfect the cut edges of the wood? Can you tolerate the imperfections for this look? The final solution is the one you'll be able to live with and be within budget. Either way that is a beautiful floor! I hope you keep us posted. https://sccpublic.s3-external-1.amazonaws.com/sys-master/images/hd9/h5a/8916622573598/Profile%20Brochure.pdf

The in-floor radiant heat is going to be the BIGGEST issue. I would look at a high-end laminate that is relatively thin (8mm or so). The thinner the material the BETTER the heat will move THROUGH the product and into the air. Carpet does well with in-floor radiant heat because it airy (lots of holes in the weave of the carpet to allow heat to pass through). Most vinyl products do NOT like radiant heat. Many engineered wood floors do not like radiant heat (it is a very 'dry' form of heat = very hard to keep wood moist and happy). A beautifully manufactured laminate will give you all the wear and tear necessary and will be LOW VOC (or no-voc if you work with Swiss manufacturing = www.lico.ch). I've seen the chemical report for Lico floors...it is MIND BLOWING how low the VOC content is. It is better than E0 (the highest known rating for flooring Europe has = 20 years ahead of CARB II). Anyway...your infloor radiant heat is a cursed blessing. The curse is your limitations for your flooring (carpet is awesome; laminate is fine; vinyl is super picky and engineered hardwood is sometimes allowed with plenty of caveats that are hard to maintain).

I had tile in my last home and moved to a home with carpet everywhere but the kitchen (yes, even the bathrooms had carpet (yuk)). After 20 years my joints could not withstand the impact of living on tile floors. Choices were to replace the carpet with Carpet - It is soft and quiet. It gets dirty and is hard to get clean. Muddy paws from an active puppy while delandscaping the yard was a nightmare. Hardwood - much more expensive - harder than tile or LVT to maintain, would require purchase of area carpets to protect. LVT - cost efficient - low maintenance, limited lifespan (20 years ish) I'm 59 - 20 years I won't be able to see what it looks like. Can add area carpets for aesthetics, but can eliminate the trip hazards of area carpets as I age in place. Engineered hardwood seemed to have the same cons as hardwood, but cannot be refinished over and over again - thin layer of wood. I decided to replace the carpet with LVT, I am doing one room at a time as I renovate, but am very happy with my choice. I bought Downs H20 from Cloister's Flooring America. It is waterproof and is manufactured by Coretech for the CCA Family of flooring companies. Same product, different name at each company website. Different price at each store (store not company level, two different Flooring America franchises had 2 different prices). Difference from highest price to lowest price was a difference of $2.00 per sq ft - I was covering 2000 sf, so this was a substantial savings. I loved the franchise I picked - Cloister's Flooring America. Other franchises really pushed the professional install - Cloister's seems to cater to the DYI folks (Owned by a Mennonite family). For $75.00 they send one of their installers out for 2 hours to teach you how to lay the flooring and they will rent you a tool kits that has everything you need to lay your floors. I bought one box of each of two colors and could exchange the one I didn't pick when placing my full order. I also got an additional $500 off because I hadn't placed my order yet and they called because they were having an anniversary sale. I hadn't called because I had a heart attack and was in the hospital when I got the call. They gave me the $500 off and told me I could call when I was home and feeling up to ordering even though the sale was just for the week. They even helped me with the layout plan. Told me to use graph paper and tracing paper. I drew out my floor plan on graph paper and traced the outline of the flooring pattern on the tracing paper. You place the tracing paper over the floor plan and move it around until you have a placement that doesn't leave you with little 2" strips anywhere. You do have to be exacting in your measurement and drawing of the floor plan and lay out enough pieces to get exact measurements for your tracing. I didn't find this method on the internet anywhere - most have you plan from the center of the room, but this worked out really well for me.

I think reading this article might help you Floating floor