I wanted to come back with an update reporting my experiences with my version of a solid-side basket (in case anyone cares).
Rather than buying a sheet of stainless or having my BIAB Mesh Basket permanently modified, I purchased a sheet of HDPE from Grainger (like McMaster-Carr). It cost me $10. The upper temp range on HDPE is high enough that there was no risk of melting or softening the plastic during the mash or mash-out.
Anyway, I cut it so that it would fit inside the basket. I warmed the edges to make the corners bend and its natural desire to expand outward made it fit snuggly inside.
I used it for 4 batches...and honestly, don't see much benefit to it. I actually got slightly lower efficiencies with it and was not able to run my recirculation as fast. One thing I did notice though was that the wort cleared up quite a bit faster during recirculation. That said, once the basket gets raised up out of the kettle during for draining/sparge to prepare for the boil...all bets are off. Both methods produce a cloudy wort. It was NOTHING like what I used to get with my pre-boil wort on my previous traditional 3V system. It's a sacrifice I have to make though for the ease & simplicity of BIAB.
Anyway, just wanted to let you all know that there's an uber-cheap way to try this out temporarily if you want. The HDPE sheet was easy to cut, didn't require welding, didn't require permanently modifying my BIAB basket, and made trying out a different method simple.