Mike,
Depends what you mean by "shimmy"
One thing you ought to check. There is a rubber block mount at the back of the tranny. It's a kind of an isolator block.
This thing can break. It tends to shear, and sit there looking like it was all right, but moves under torque load.
What I'm suggesting is, if this part was already broken, then your leaking tranny fluid may have flowed back there and into the shear layer, with the result that it now has lost even the grip that the rubber-rubber surface was giving you.
Could be totally wrong, but it is worth checking out. [along with all the rest of your engine mounts while it is up on the ramp.]
Joe
__________________
Black Betty [Bam a Lam!] '93 UK spec, still languishing
Betty
Jersey Girl Silver '92 UK [Channel Isles] 40K
Jersey Girl @ Mersea
Candy Purple Honda Blackbird
Plum Dangerous
White X2 RVR Mitsubishi 1800GDI.
Vantastic
40,000 miles Jersey Girl