I've repaired tanks before, and quite frankly replacing the bottom is a lot easier than the side panels. At the very minimum you should use double strength glass. 30 gallon tanks usually don't need tempered glass. The biggest hang-up I've found is getting the glass cut right. If you find a glass shop, bring it to them and tell them to cut a piece that fits. It may cost a bit, but it is well worth it.
If you have enough room, you might not have to remove the frame. Just angle it up through the bottom. But before you do this, have your bead of aquarium silicone sealant in the channel of the bottom frame. Don't skimp on it . . . you want it to ooze out when you set the glass in place and press firmly until the silicone squirts out the bottom of the frame inside and outside of the tank. Make sure it is firmly seated and no airbubbles . .. if you use a lot of sealant you won't have to worry about air bubbles.
Pay special attention to the corners. Smooth out the stuff that has oozed out and remove the excess. I use my finger for this. It works better than any tool. Let it cure for a good 72 hours in a warm dry place. Support the bottom on the edge of the frame with bricks or something . . . so you can look and feel under it. Fill it with water. Check for leaks . . . let it stand filled for a few days . . . checking each day for leaks. If you used enough sealant, you won't find any.