I would say there is: create a compiler for the ISA that only uses as many 64-bit registers as a 32-bit CPU has, and only use the additional 64-bit registers to perform 32-bit calculations.

As far as theory goes, as you say, one of the reasons 64-bit is faster is because it can operate on 64-bits more efficiently than a 32-bit processor (because it has more registers that are 64 bits wide). So if we can split up, for example, a 256 bit bignum operation into two instructions instead of four, that should -- more or less -- half the execution time. But yeah, I have no idea to what extent this effect influences how fast various operations are done.

Another factor, that I think is often overlooked, is the width of the DRAM-to-CPU interface. Memory still is the bottleneck of most systems.

A 64-bit CPU should also be slower at some things, among other things because describing a memory address requires transferring twice as much data to the CPU. But again, I really have no idea how much of an impact this really has.