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.

The pricing for the electric radiant heat kind of depends on how many twists and turns you have. The way it works is it comes on a large roll, which gets cut each time a turn is necessary. If you have a lot of turns, you may need more material. Also, you don't have coverage in areas where the cabinets/island are. So I calculate your room as being 238 sq feet, but I have no idea as to how much of the floor space is occupied by cabinets. That needs to be subtracted. I bought ours from warmly*yours.com and they offered a 20% discount for contractors. Figure out from your floor plan how much walking space you have - you can include or exclude the space under the toekick depending on whether your feet ever go there, and enter the area on the estimate tool on the their website. I don't think an estimate of $1000-$1200 would be too far off. Add to that price the cost of the thermostat as well, and the labor for your guy to do the work. It was definitely worth it for us in our bathrooms - one bathroom had two "cold walls" or outside walls, so I wanted maximum warmth.

If the unfinished part of the mostly is mostly below grade, then it will be naturally cooled by the surrounding earth. There should be no need to add any cooling. Where in the deep south are you located? For the finished section I would recommend adding a zone off the first floor system. In the winter it takes very little heat to keep a basement warm especially in your climate. In the summer it will help dry out the basement.

If you want the STRONG GREY colours shown in your photos, you will need to work with factory finished. If you like the liming or cerusing effect (the white in the grain) then you will need to work with the factory finish. I've heard of a small handful of HIGH-END professionals who can achieve these looks on a site-finished floor. If you think that the population of the US+Canada is around 375,000,000 that is a SMALL amount of humans....like 100-150 professionals who can handle a job like that. Imagine the price tag! We will see this level of workmanship on $25Mill homes. The price of the professional is not at issue in a home that has multiple millions of dollars in financial backing. I understand your Project Manager's concerns. Repairing damage to a factory finished floor isn't fun...but it isn't difficult either. The worst case scenario = cut out the plank and drop another one in. A bit of glue...a bit of waiting and everyone's happy. I'm not sure why the push back is so hard (the PM has probably had something go wrong in the past and had it bite him/her in the arse pretty hard). So long as you assure him/her that you will pay for all the damage control (ram board, etc) you should be fine.