Shock/Shudder on Quick Clutch Depress Under Load

Say you pull away in first moderately quickly so there is load on the engine. Now, as you hit ~4k, you depress the clutch quickly to change to second.  In my car, when I do this, there is a sudden strong shudder when the torque releases (I'm not even sure if that is the correct terminology?).  There seems to be some play in the mounts.  If I rock the engine back and forth by hand, I can hear squeaking coming from the lower bay so I assume it's the dogbone mount?  Could this be related?  I've a yellow powerflex insert, but I've put off fitting it due to the reports of some people saying it makes vibrations intolerable at idle and reverse etc.

What else could I look at?  I'll get some VCDS logging ASAP.