It can be done
Ive patched side cracks before with no problem
I think if you use a piece of at least 1/8" thick glass and patch it on the inside of the tank and then place a piece of foam (like the pink foam & NOT styrofoam) on the inner bottom you should be fine.
I would go to a local glass shop and have them custom size a glass pane the size of the inside of the bottom and just silicone that on the cracked bottom.
Just be sure to use aquarium safe silicone (Silicone 1 by GE ) and put a good bead along all the cracks.