I then considered the ability to send another amount, say a token 0.01 BTC, from the same address that my earlier payment originated from. Even if I were able to force bitcoin to use a specific address for the input for the transaction, that transaction would then be recognized as an attempt to double spend and thus wouldn't be honored or relayed by any nodes.
If you were able to force Bitcoin to spend from a specific address, and the person asking for proof first sent 0.01 BTC to that address to send back, then it wouldn't need to be a double spend.