Shouldn't be too hard mate, I dont understand exactly what you mean about snapped lugs, or the hole in the floor (I take it that was in the donor vehicle).

But yeah you can get that in without removing the dash (easier with the glovebox out) - but its not the way to do it. Taking the dash out is usually quicker than the stuff around - its half disassembled once you've got the glovebox out anyway.

You obviously want the demister to work, so the ducts and plastic bits need to line up properly nice fits, no gaping leaks, nice and straight, and you may as well check all the cables are working properly once you finish the job (they're simple, but easy enough to dislodge or wedge/twist/jam if you cant see your final result), so, I'd just take the dash out, (have several marge containers or etc to put the different size screws in and know where they came from) and then you can set your demister system up properly, and be confident its correct.

Taking the dash out is less than an hour if you're organised, putting it back same time. You could easy spend heaps longer tryna manouver the duct in with only the glove box removed, and you may not get it in the right place, (and you get to clean your air system out at the same time. - it is bound to be pretty dusty).