The 2-3 starts sounds like the anti-drainback valve on the top of the pump. You can see if it is that by just leaving the key on for a few seconds before you give it the extra twist to start it. If it fires right up, the gas is draining back to the tank while it's off.
The bogging down and poor idle seems to be commonly the fuel pump. Perhaps it is the cause of both issues if the anti-drainback trick doesn't work.