Finding The Inverse of The Modulo Operation
I ended up solving my issue, but not in the way I expected. The solution involves the inherent halving of the output string. Using this, one can simply calculate the quotient of dividing x by y and using that as the second alphanumeric character, forming a pair. In the given example, the resulting G would become G1 because the modular arithmetic involved looping over the alphanumeric character array once. 

The algorithm is now as follows: x % y = r + (x / y), which is easily reversible by bruteforcing the possible dividends and simply selecting the correct one using the second character in the alphanumeric pair. Thus, this modified algorithm is now reversible and has been proven to work with the example given in the original question.