Follow up on this for posterity.
Summary: Two failed PS2 1.44 drives, one from a IBM P75, the other from an P70.
I theorized that caps were the problem, as there was clear evidence of the leaked canned caps and some
corrosion on the circuit boards.
I bought and scrounged caps to replace them with. I destroyed a pad on each drive but managed to
route to the destination point of the traces.
Working with two soldering irons helped make the removal easier.
I bought some aluminum can caps similar to the originals but found that working with leaded parts
was much much easier.
The bottom line is the P70 drive did not respond, but the P75 drive did.
Unfortunately, the P75 is dead, so the good drive went into the working P70.
Here's the photos, the caps installed in the fixed drive is in photo #5.
http://imgur.com/a/GneNM
So it is possible that failed PS2 floppy drives can be fixed simply with new caps-
maybe not all of them, but this is evidence that some can.
Next it on the list is a IBM Convertible with at least one non working drive.
Hopefully I will succeed there too.