There is a procedure for implementing changes to code, but a consensus cannot seem to be reached.

A consensus has already been reached. Actually it has been there all along: the decision of letting the block size unchanged.

It's a stalemate in the most profound sense of the word.

It's not at all a stalemate. Core is shipping improvement after improvement: CSV, CLTV. Segwit have paved the way for Lighting that will increase the network bandwidth by orders of magnitude making the blocksize debate moot.

So what can we do to end the Bitcoin Blocksize debate?

Wait. There won't be a debate anymore once Lighting is live.