Uhm, this is what i did 2 weeks ago.
I found that the outside bottom corner broke off a bit.
The inside of the silicone was still ok.
I vacuumed the corner and took away any loose fragments of glass.
Then i filled in the missing pieces with silicone and let it dry a bit.
I did a second thick layer while the first layer was still soft.
I flattened the outside with a wet finger and left the whole thing to dry.
The whole tank is sitting on a half an inch styrofoam and i took the risk for i know the inside silicone was still perfect and that I'd be watching the tank very closely for i had a new fish in there .
But after rereading your post i can only safely suggest to cut out all old silicone, reseal the tank and get a proper stand before you start the resealing.
There's no quick fix solution to your problem, and of one thing I'm sure in the hobby, your fish will ALLWAYS need water and leak getting worst suddenly, like at night,and the possible result of dead fish is surely gonna spoil your day.
Better being safe then sorry.
No chance of your LFS taking in your fish for some days while you reseal?
I often see fish on holidays at my lfs!