Bruteforcing a solution until hashes match doesn't work. If you try to bruteforce X bits and use a hash of size Y for validation, you will get 2^(X-Y) possible solutions.
(I made the same mistake some time ago when I tried to bruteforce a 4 byte RC4 key with 3 known bytes in the plain text; I found 256 solutions.)
Yes, if you want to be sure that your solution is correct, you must run the compressor yourself. Then you count the number of collisions it takes to happen upon the correct solution and feed this counter to your decompressor. But then you place the burden of solving the halting problem on yourself and then you got more serious problems than compressing random data.
(I made the same mistake some time ago when I tried to bruteforce a 4 byte RC4 key with 3 known bytes in the plain text; I found 256 solutions.)