Is this an ignition problem?

I have been having this on going problem since supercharger install. Car will "spit and sputter" at low rpms and shake at idle. When I try to get into boost it will fall flat on its face. And at cruise I will get an occasional miss. Car will not start very good after it gets hot sometimes not at all (but turns over). I will crank and crank and won't start but as soons as I disengage the starter it will start. It seems like it will run different day-to-day.

I have new cap, rotor, plugs, and wires. TFI module tested good. Will do it with the vortech BTM connected and disconnected. No codes and cylinder balance test passed. Compression good in all cylinders also did leakdown test which also looked good.

I need some help, could somebody point me in the right direction? -distributor, coil, do I need a ignition upgrade? Anything else?

Or could it be a fuel problem?

Yes fuel pressure gauge in use.

I have been thinking that my coil may be going bad. When the starter is engaged less voltage getting to coil reducing its output even more. A slight voltage drop on the primary would cause a significant drop on the secondary coil, and if the coil is on the fritz and has low output already this would cause problems and explains why as soon as the starter is disengaged the it fires, right? How sensitive are coils to temp changes (if they are broken down)?

Thanks