Excuse me if I am misunderstanding your approach completely, but it makes no sense to me, why would you want that all measurements are the same, why then measure at all? If all genes have different measurements, there can be no random downsampling such that all measurements are identical afterwards, even if including rounding error. With FPKM these values should be even mostly unchanged by downsampling, because the division by the number of reads, which would be less for downsampling.

Say we have gene a of length 1kb, you sequenced 1 million reads, and a has 1000 reads, while gene b also is 1kb but has 500 reads, so gene a has 1000 FPKM and b 500 FPKM, say you downsample - truly randomly - 10% (100,000 reads) of all, what is the expected value of reads for a and b? well, say it is 100 and 50 respectively, but you also have only 100k reads, so the FPKMs for a and be will be 1000 and 500 with the expected value of downsampled reads.