I'm experiencing a similar behaviour with my A1200. In particular, it shows a flickering pointer while drives work.
It seems a GND problem.
Let me know if you solve in some way and I'll do the same.
First of all check if your plug has all its three pins (the third, obviously, is for the ground...).
After, if you have a meter, try to check if the Amiga's ground contacts with the PSU's one (if you're using an external not-Amiga is more simple to test otherwise you should to screw it but... warning to your health!!! :-D ).
You said you're experiencing the problem with more than one PSU, so the problem is not on the PSU connector but it should be on the internal contacts of the Amiga connector. I'm not referring to the contacts with the motherboard (that you have resoldered) but those inside the connector itself. You'd try to move a little the plug and connector while the Amiga is turned on to see if changes something.
Last test, measure the two voltages (+5 and +12) on mobo's floppy connector and check if they are constant. Check also (when the Amiga is turned off so it's safer) if the two internal pins of the connector contacts with other Amiga's ground.
Keep me update!
Alex