Since that is fundamentally my own problem, and I have to deal with it over time and within my team's constraints, I didn't want to bore anyone with the details of why I don't just update the gem.
Thank you for the reply/help, but my question remains: Is it possible to use the these kinds of patch files on Heroku, and if so, how?
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EDIT: Responding to tomfakes here since HN won't let me:
I am only going from 3.2.2 to 3.2.11. I think the breakage is query-related, and it's actually quite embarrassing how bad so much of my old code is (procedural doesn't even begin to describe it). But this is how one learns, I suppose, and now I'm very incentive to go back and refactor/fix all of it.
I'm just worried about the in-between time, and bothered that this process of "applying a patch" is a mystery to me.