It would seem to me in this day and age that the word "no" or "not possible" is a term used only be either the close minded or the plain lazy.
I myself dread the days when a small crawlspace install is coming up, but I none the less go and do it.
It sounds to me like you want radiant 'cuz you know it's the best and that's what you want. You also sound willing to take measures to get what you want. This adds up to a smart consumer, and a flexable mindset.
Which is why I would suggest other options and you can take what you will from them.
It sounds to me like your first option in this remodel is to look into expanding the crawlspace. I know it might sound like alot to the average laymen, but it's usually not all that bad once the numbers are in. And considering the outcome of having full access under the house..........it seems like a viable option at the very least.
As a heating and cooling contractor who deals mainly with the extream high end homes and projects, I will say that many times there is an answer.....it's only a matter of you asking the right person who has it !
At least 90% of the homes I do have radiant heating in them. I have learned quite a bit about it since working with these contracts. Which is why I say that if you can achieve even the smallest amount of room under your home (crawlspace), then radiant is an easy option. The underfloor plates can easily be installed on one's back and icynene will obviously be easy as well.
And with this new underfloor room you'll have aquired, air conditioning will also be a simple option as well. Unico can easily be installed in a space like this and provide you with excellent comfort, not to mention can be used as a suplimental backup heat if your home is one with large foyers and greatrooms and areas of such nature if your contractor has any doubts as to radiant abilities in the coldest days.
In short, achieving a little more room under the house can get you alot more comfort in your home.