I've been able to recover some binaries that I'm not sure how to get converted back
If you have the binary representation of a private key, then you can convert that to hex and import it into a wallet. You could even generate a public address to check if there are any bitcoin in the address first.
OP never say he managed to recover 256-bit of private key or binaries which represent private keys though. Besides, you'll need to convert the binary to WIF which is supported by more wallet these days.
Working with the hard drive, unfortunately all I really remember is that I stored the keys and other data in binary and hex formats.
Assuming you directly store 256-bit private key, rather than WIF or different private key format which have specific prefix/magic bytes, i don't see how anyone could do search effectively.
You've nicely summarized one major issue here in a succinct way.
In this case, there's little you could do. Performing sliding window (with 1-bit window) on entire HDD to get list of 256-bit of data would generate trillions of private keys if my calculation is correct.