acceleration hesitation yet RPM's respond

It sounds like a transaxle problem (low on fluid or low line pressure). You'll need to get it scanned for DTCs. The PCM keeps track of shift performance and thus troubleshooting has to start with the stored code(s).

2004 is when they went to the throttle-by-wire in which the PCM does what it wants to do. One scenario is, the PCM keeps track of shift performance and adjusts the line pressure by the pressure control solenoid. It's possible that the fluid pump inside the transaxle is not generating sufficient pressure at low input shaft speeds even with the PCM commanding maximum pressure. The shifts are then being delayed.

Fake tachometer? That's too spooky. I actually have a Tiny-Tach for small engines (don't laugh). I wonder what I'd see if I were to hook it up. Anyway, the transaxle was what popped to my mind based on the age and mileage of the vehicle but who knows?

It has a flexible pickup cable that's normally wound around the ignition wire. I think it picks up the RF spikes and thus will work if I get it around or near the ignition coil. I actually haven't tried it, of course.

There aren't any common transaxle problems per se. The thing is, DTCs may be set but the CEL will not turn on unless there's a problem with the emission control system. As I've posted before, it'd be best to get it scanned for any stored DTCs. In addition to the current codes, often historical or pending codes tell a story as well.