OK I had a very similar problem. Mine would just quit for no apparent reason, and then after 20 min or so it would start ok.
After a very long and difficult diagnostic period, including replacing the fuel pump 3x, we finally found the following: intermittent open in the wiring at the connector on the fuel sender assembly, which includes the wiring for the fuel pump. That your fuel guage is 'all over the place' may mean you have a similar problem (the wires for the pump and fuel guage all come through the same connector.)
The bad news: no way to replace the connector separately, and GM wants $460 for a new fuel sender assy--and that is without the fuel pump.
I found that the aftermarket now makes the assembly for about $80. I have one on order, supposed to be here monday, then we will see.