Cool idea. I'll bet you could get a sheet of plexiglass cut at the hardware store to fit any bag. They might even round the corners for you if you asked or you could file them down yourself. I've got a giant felted Noni tote that needs a bottom like this, but none of the sizes listed on that site would work for me. Interesting...
i've actually tried something as suggested here...the only problem i find is that stuff works it's way underneath the insert and you have to remove it to get whatever is hiding....must be a better solution...other than actually lining the darn thing. sometimes i do wish for a stronger, more form-maintaining bottom (on my bags as well as my own body!)....anyhow, the only other thing i've done is to buy a small light-weight basket and stuff that inside for stability.
I've used the plastic mesh canvas for cross-stitching, the thickest I can find, for bag bottoms. You can cut it to size, cover it with fabric and even stitch it to the bottom or sides of your bag if you don't want stuff getting under it . Don't know if it would be stiff enough for a really large bag but if you could double it.