first, my regex is not perfect, there are ways to make it faster (making it greedy and starting only from start is a good start). but anyway it's slow.
regarding what you are going to do: first you want to use a 16bit MD5 and the count of ones and zeros. the worst case is having all 26 ones or zeroes, so you need 5 bits for that information: that mean for 26 bit of data, you'll get 5+16 bit result. that's about 20% compression.
unfortunately, you can't guarantee that for a given MD5 and number of ones, you'll have only 1 possibile 26bit data. you could analize it and findout how many case you can have at worst and i fear it's more then 32 (if it was 32, you had need another 5bit and the total of data would be 26)