I finally got an agent to dig into things, and apparently an in-cabin pet on your PNR inhibits CPU eligibility/processing. You can have an agent at the airport add you to the list, but since cabins get mostly filled by advance CPU this likely means that you're going to be stuck in the back, or be given the last seat which will likely be a no-go for your pet (bulkhead). Especially when you're traveling with another passenger, and you want to have two seats together. I suppose that's just the way it is, but frustrating for two 1Ks to end up sitting in E+ on a route that often CPUs silvers...

The two obvious alternatives are to either wait until the CPU clears to add the pet to your PNR (but risks the flight being "at capacity" for pets already") or to take this as yet another absurd incentive to consider going the ESA route and stop playing by the rules and paying the in-cabin pet fee--which as an aside is just a mega pain logistically: no OLCI, no electronic boarding passes, and now no chance to be CPUed (on top of being charged a fee for literally no benefit).