Third time's a charm! The Apple IIe is now successfully booting with the parasite implanted within.
The first two attempts failed with the processor apparently halted. It turns out that the pullups and pulldowns I was using were way too large (27K) to deal with the load they were driving; it's unclear whether it was something weird about the OE pins they were pulling or the uninitialized GPIOs they were interfacing with on the RP2040. I just added some code on the RP2040 to pull the pins in the right direction at startup, and they get set up quickly enough for the machine to start.
The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!