Even without doing any filesystem tricks, the challenge seems quite possible. While it's true that writing a compressor that compresses all input data is impossible, this barrier is removed because the compressor only needs to work on a single file.
Mathematically this has non-zero (albeit very small) probability but I'd wager that even having such file it would be unfeasible to find its compressed form. Maybe the file is the third million of bytes of pi squared, but how do you find this fact?
So by the very nature of it if your decompressor is non-zero in length, you have to find some efficiency/tricks to make the file smaller.
Realistically the overhead on the decompressor will be 10 KB and that is before any kind of actual logic, so you are looking at shaving a minimum of 50 KB off of the original file (which is completely random).
So if, for example, 2% of files can actually be reduced in size (I don't know what the actual number is, and if it is even computable) that's still positive EV in a $100 vs $5000 bet.
That is, if the file was truly random, it would have a chance of 1/(2^X) of being all 0, where X is the size of the file. But since Mike would reject that file, the chance is actually 0.
Same for all files with easily exploitable patterns - for example, I am sure that Goldman checked that the file could not be compressed with gzip before sending it.
So the EV is probably not positive, even if there is a small chance that a random file of size X can be compressed.