Yeah, but a built-up cover won't help against flexion much - better off fabing a truss. Or buying something like a RuffStuff cover - which looks to be tougher than the Hinges of Hell.
What you're mainly going to be after is protection against impact - which is why you don't need the whole flange (leaving the flange in place will make it harder to stack the covers from the off anyhow.) If you want impact protection and anti-flexion, make a cover (or just buy one.)
For your needs, stacking covers will probably do for the moment (until next year's tax rebate. You spend a lot of time upside-down on a mortgage, and interest on a home loan is usually deductible.)
To maximise impact protection, leave some flange on the second cover - that allows it to brace against the housing in impact, doubles the bracing it gets (from the original cover,) and you still have the "more metal better" approach. That isn't always true - but it's true enough in this case, and I doubt you've got the wherewithal to engineer a new cover.
If you want to really do the job, use the bottom half of the second cover, then run a section of angle iron bent to follow the contour of the cover, angle "point" outwards, and lay it right about over the ring gear. That gives you an extra bumper, works as a stiffening member, and gives the ring gear a little extra protection as well. I'm assuming you already have fab tools (welder a must, torch a help with bending.) You shouldn't need to heat-treat the thing, since you're going to get more strength from the shape than the material anyhow (see why I mentioned engineering?) Using a half-round section of pipe would be a bit stronger, but it's more work.
Whatever you to, make sure you seal against moisture intrusion between the layers! Make sure it's dry, and fill the area in between with some variety of "blow-foam" fill, and then seal shut (or make sure the area between is dry, and seal with a continuous weld bead - but then you run the risk of warping the cover.) Getting moisture/water in between the layers will end up failing both layers - even if you've painted them (paint just delays the inevitable, in this case.) That doesn't mean you shouldn't paint them as well - but apply some thought once you're done letting the paint dry. A couple of extra bucks will save you much more later.
Ideally, you'd want something like a one-piece cover stamped from something like 1/4" or 3/8" plate, but that's impractical (do you have any idea just how much force you'd need to stamp it to shape? Ouch...)