Welcome to the board
By the look of things under the hood, it appears to be unmolested for the most part. Bummer about the frame. I agree that it may be better to get another frame.....that is if they are easy to find in your area.
As for the trans, any other trans that has the same shifter location isn't going to shift much better than the SM420 that is most likely in there now. If quicker shifts are what you're after, then you will need to look for a car 4 speed. They will fit without a lot of work, although the shifter will be close to the seat. If your budget allows I would consider something like the Tremec 5 speeds.