I agree with Arthmoor's concern about modifying game.pex, but:
a) that's where the broken API is defined, and
b) this patch is a temporary measure, not long-lived like SKSE64 or USSEP.
I continued private testing on the Xbox One console and also researched saved games.
Adding and removing the patch repeatedly from the load order does not cause any apparent problems in game on Xbox One. When the patch is active, Campfire and Frostfall work properly. You can harvest wood, use cookpots, get warmth from fires and access Campfire perk trees. When the patch is removed from the load order, all those features are broken again, but the game otherwise plays properly.
The FindRefAPIPatch.bsa archive contains four scripts:
_frp_game.pex (a shim loader to get a reference to the main quest)
game.pex (fallback to patch ONLY if native API produces no result)
On PC, inspection of saved games using Fallrim tools ReSaver (v2.9.8) shows that game.pex and _frp_game.pex are never persisted to game saves. Only the quest scripts and associated references are persisted. In a game save created after removing the patch, ReSaver reported 17 unattached instances that use roughly 3-4 KB of space (based on file size comparisons).
I'm much more confident in this patch now. When Bethesda releases an update with the API fix, the patch will use the native result automatically. When Xbox players remove the patch, it will leave behind only a small amount of bloat in their game saves. The patch description can and will provide information to let Xbox players make an informed decision about whether to use it.
Does this information change the calculus in any way?