I agree with the above.
This should be an easy problem to diagnose (easier said than done, right?
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).
I would disconnect the mag wires and try to start it. If it fires that time in the start position, you KNOW it's a wiring problem. If it doesn't, you KNOW it's a mag problem.
Next I would disconnect the starter contactor wires, then put a multimeter on the mag wires. Check all five positions on the key switch, OFF, R, L, BOTH and START. With regard to the mag wires,
they should be identical in the BOTH and START position if you have dual impulse-coupled mags. You mentioned that you replaced the left mag? Do you have the little jumper installed on your keyswitch for disabling a mag if you only have one impulse-coupled mag? If you have
two impulse-coupled mags of course this jumper should not be there. You should be starting on both mags. I have the same same setup on my XP-360 w/ slick mags. Prime for three seconds in winter, 5 seconds in summer and BAM...that thing fires up with no hesitation whatsoever...always on the first or second blade.
Right now I'm wondering if you're every really running on both mags. It wouldn't be unheard of. One of our local guys flew his entire Phase I on one mag due to a wiring problem. Do you notice an RPM difference when you switch between the two mags?
With the engine idling, I would also briefly switch the key switch to off to see if it actually tries to kill the engine.
This problem is gonna bother me all day.