Question - if you push down on the gas pedal and force the transaxle
to downshift to third gear (while still in overdirve mode) do you
still get that chatter?

If the chatter goes away in 3rd gear but still in overdrive mode,  I'd
suspect the 4th gear clutch has a problem. If you still have the
problem in overdirve range but in third gear, more likely the 3rd
roller clutch is not holding. The power flow is different between 3rd
gear in overdrive range VS 3rd gear in drive range: in 3rd gear in
drive range the 4th clutch is not applied and 3rd roller clutch is
effectively locked by the input clutch..

Neither is a cheap repair - either would require removal of transaxle
and a teardown (though the 4th clutch is the first clutch in the
gearset). . I'd first have the pan pulled and the filter assembly
replaced, since low line pressure (which can be caused by a partially
plugged filter) can lead to  clutches slipping. Look CAREFULLY at the
pan for signs of either excess metal debris (which points to the 3rd
roller clutch) or excess friction material debris (4th clutch).

130K on a THM440-T4 before rebuild is actually not too bad

Hope this info helps.

Regards,
 Bill Bowen
 Sacramento, CA