decryption many time pad
This sounds suspiciously like the first extra credit assignment out of Dan Boneh's Cryptography I on Coursera.  Dan gives you a great hint in the assignment listing for this one.  Take a look at an ASCII chart and note what happens when you XOR something with space rather than with an alphanumeric.

Once you've got that sorted out, your best bet is to XOR things together, as you suggest, and use the knowledge gained from Dan's hint on XORing with space to build a histogram of candidate plaintext characters for each position.  My first cut at this assignment got about 85% of the characters, and filling in the rest was simple due to the common digraphs of english.