Thanks for the input. Perhaps the best idea is just to go custom in this case, or build it myself. I will continue to explore my options, though.
You may have to go the self-build route that Orvilleowner was talking about. Another Forum member, Shreddin, recently tried to put in an order to the Custom Shop for a Strat with very particular - though not outlandish - specs. He found that not only was he quoted an enormous price, the CS wouldn't do everything he required. (Check out that thread under Shreddin's name...)
The Custom Shop steps beyond what's available in the regular catalog - but nevertheless keeps within the Fender mould. If it doesn't qualify as their idea of a Strat, Tele, etc they seem uninterested in doing it.
Don't know which side of that line a throughneck Strat would come, but since like the others I don't remember seeing one I fear it might be outside their remit.
Still, over on the Custom Shop Forum you will find folks who have a better idea of what the CS will and won't do. Or just ask the CS themselves...
Cheers - C