If you are determined to keep the mechanical pump, I would install an electric pump with a check valve at the electric pump side and install a relay with a timer circuit for 5 sec.
Every time you turn the key the electric pump will cycle for 5 sec priming the fuel bowl. If you really wanna get trick install a temp switch that will only allow contact at 120 degrees or below. This will only allow the pump to run only when the motor is dead cold.
It seems like a alot or complicated but it really is not. Besides you can always stay with your mechanical as others have mentioned but where is the fun in that
What ever your choice we are here for you.