Prior to switching to the Foundry, I did no-sparge in a cooler lined with a BIAB bag. I always squeezed my bag like I was dying of thirst and it was filled with Bear Grylls pee. (If you don't get the reference, be thankful) I can't say that I've noticed a difference in flavor using darker grains with the Foundry (no bag/no squeeze) vs bag-squeezing. I haven't brewed a porter or stout with the Foundry yet, but I've used plenty of darker crystal malts like C-120 and Simpson's DRC.
Even if these malts potentially do release some harsher compounds if squeezed, keep in mind that the bulk of the grain bag is going to be base malt and that could potentially end up filtering out much of these insoluble compounds. The two bag method sounds interesting, and I'd love to hear how the experiment goes, but in my experience I don't know if it's necessary.