Gordon,
What you're describing is possible, and I think you're on the right track. As long as your constants are always in the same order in memory, putting them in a separate flash sector and updating only that sector shouldn't be a problem. Probably the easiest way to do it is to make a linker command file that loads the other unwanted sections into RAM or an unimplemented part of the address space. You might try the block starting at address 0x14000.
Please let us know the results when you're finished; other people probably have this same question.
Thanks,