Hesitation when starting

I think your cap idea would work.........if you do thus:

You need power both in start and run, so I assume you now longer use an ignition coil ballast?

If not, wire the original ballast brown and blue together, which will give you power in both "start" and "run" but with the short switching time in the switch

Take that point and run a series diode, Radio shack, etc, say, a 5A rated diode, with the banded end towards your ECU, and with your cap on the ECU side of the diode.

the diode will isolate any discharge load from the rest of the ignition run buss, so the only cap discharge path will now be through the ECU