Run, don't walk from that transmission shop!
If you browse this forum a bit, you'll see that a lot of people actually prefer the 200R4 to the 700R4. The 200R4, properly built, can withstand huge amounts of HP & torque, plus it does have better ratio spacing between gears than the 700R4. Why a shop would recommend doing a different transmission & having to mess with crossmember location (IIRC) & driveshaft length issues, is beyond me. Unless they're going to nickel & dime you to death & have you out the door for $3,500 by the time they're done building & installing the 700R4. Sounds like they're either lazy, incompetent, or crooked, and maybe even more than one of those! Maybe all of them!!
Post your location & maybe someone on here will have a local recommended trans shop for you. If not, try to seek out some local hot rod folks or racers that can point you to a good trans builder. If you are willing to do the install, someone on here posted the name of a builder that can ship you a fully built trans for a reasonable amount.