Couldn't we use some of the more interesting signature types (ANYONECANPAY or something like that)? People could sign a transaction with their one input they're putting in, their output to themselves that they care about, 1 BTC to you, and you then just add your 1 BTC input from any transaction you want.
If we use "SINGLE|ANYONECANPAY" then we can each make a transaction with 1 input and 1 output which just sends our BTC to ourselves, and gmaxwell can combine them all into a single transaction. I think.
"SINGLE" meaning "I don't care who else gets paid, so long as I get my BTC", and "ANYONECANPAY" meaning "I don't care who else pays, so long as I pay my BTC".