Well, after several weeks of testing, I'd have to say the results are interesting. The power supply with the higher amperage rating has always charged the phone, but so has the stock supply... most of the time.
I've tried different batteries, different cables, and different chargers. Just based on what I've seen, I will continue to use the new power supply. No longer having access to test instruments I can't explain why the original one doesn't work some of the time. There's a small chance it could still be a mechanical issue with the phone connector.
So. No conclusion in the short term. If, after several months, the present setup has worked fine, then I'll conclude the OEM charger was a bit flakey, but we will see.