ajoeiam,
"- - - how does having a tool opposite the one in use on a 4-way toolpost improve rigidity?"
The 4-way toolblock and mounting stud on 7x mini lathes of mine's vintage are too "flexible" to begin with. I also suspect that under cutting conditions they may oscillate (which is what chatter is.) So, the logic (which is not my original idea) is that equalizing stress on the block and "balancing" the assembly will reduce chatter and make it easier to keep the cutting edge(s) of the tool aligned when cutting. And, the cutting stresses change with the usual feeds and speeds and type of material being cut.
I will admit that other factors come into play, especially if I have the "wrong" toolbit or have it ground wrong or etc. or etc........
I have tested the "second toolbit installed opposite" theory on my lathe in my shop and it helps in my situation: Your mileage may vary...
I also made a "one toolbit" toolblock that was all solid except for a mounting slot for one toolbit and that performed better than the stock one.
When I got the QCTP, I found it came with a heavier mounting stud made of better material and just seemed to be more rigid in its construction. It is a wedge type toolpost, rather than a piston type, which was my preference. I can't comment on the performance with a piston type toolpost.
--ShopShoe