If you want to keep the "upgraded" cotterless BB, you will want to make sure that it gives you the correct chain line. I'm most familiar with the early to mid '70s Gran Prix. According to my notes, I've measured the chainline on a GranPrix at 44mm.
The Gran Prix BTW has a much better front fork than the Record. I haven't seen a Record yet that doesn't have a bent fork. They are quite weak and prone to bending.
I believe the Record and the GP had the same 26 tpi cup and spindle cottered crankset.