Try to find a " Right Grip ".
"At the very least, is the problem tempered with a heavier lens (I've affixed a skopar 21/4 and am hoping that the problem will be exclusive to it and similarly weighted lenses)? "
Yes it's better-
It's not a design flaw per say just that the balance is optimised for fast normal lenses which happen to be pretty dense. It's fine with the 40f/1.4 and the 75f/2.5 for example. The extra lug on the side grip helps, unfortunately I find the grip part is too small to provide much meaningful extra grip and you lose your tripod thread which is a drag.
The solution there, is to add a " Right Grip ", along with a Stroboframe Q.R.
plate. The " R.G. ", was an item made pre digital & pre A.F., to give you a
Motor Drive type grip on Non-Motorized cameras.
Look for it on eBay, or your local swap meet. Cameras with built-in motors
killed it's manufacturer.
I originally used this, with a Canon EF, so that when I grabbed it, my fingers
curled around it, the same way they did on my motorized cameras.
Right Grip even provided a half / baked flash bracket, as part of the Right Grip handle. When a shoe is mounted this could be used to hold the spirit-level, instead of the dual shoe, which is impossible to find.
I use one of these on my Black Bessa L, along with the side grip.
It provides an even better grip, with theside grip, then without. I had a custom screw machined for these to hold the Q.R. plus anti-twist plate & side grip in place. Then I screw the R.G. into the Q.R., for handholding.
When I mount the camera to a tripod, I remove the R.G. to use the Newton Rotator, fitted with a Stroboframe Q.R. receiver, ( bottom ).
I use the same set-up on my Black Contax G2.