The original tire that came on your '77 Corvette was a GR70-15, which crosses over to a P225-70R15 in the p-metric sizes on a 8" wide wheel. In 1978, the stock tire for the '78 Corvette was the P225-70R15 and the optional tire was a P255-60R15 on a 8" wide wheel. On the '78's with the optional FE-7 Gymkhana Suspension, GM cut the inner fender well lip off on the front fenders to add clearance with the P255 size tire. The FE-7 suspension lowered the car sightly and I'm guessing tire clearance was a concern to the General. To answer your question, yes, the P255's will fit your '77 on a stock 8" wheel without clearance problems. Even if you have the optional FE7 suspension, I would not expect there to be a clearance problem on the front. A lot of Corvettes out there running the P255's on stock rims with no problems.
On the transmission - speedo question, I do not know. If the P225 has the same or close to same diameter as the P255, your speedo should read the same.
I do know that on my '72, a P245-50R15 on a stock rim will not fit in the rear due to a interference fit with the trailing arm. There are some who call BS on that, saying it should fit with no problems. But it is a '72, not a '77.