Is it possible to swap the non navigation infinity stereo for the one with navigation?

Possible, Yes. Just expensive.

I have read that it can be costly.. And I'm willing to spend the money to keep the car stock on the inside. Is it a dealership I would have to go to for this type of install?

yes but make sure it is specific with your OEM other wise it will act as if you have a short in the system. there are usually 5 years segments of vehicle production but not with Hyundai their tibruon is 01-03 04-05 and 06 then 07-09 every coupe of years the changes were enough that those in other years are not compatible with the previous years. I dont know what happened here but usually it is 00-05 and 05-99 jumps like that we are finding it almost impossible to find matching parts for an 06..tiburon. good luck but dont use a part that is not specific to your year make and model.. it will cause a nightmare.