Very doubtful it is the shift interrupt ... I've only seen one fail in my life and it was 'sticky' due to over and MIS application of BoeShield T-9 spray, which should NEVER be applied to any moving part IMHO. Static parts - OK, but nothing that moves.
That puppy sounds like she needs a tune up; first performing a sync & link, then a tune of the idle circuit of each of the carbs in sequence. After all 6 are adjusted, if you need to adjust 1, you need to go back over ALL 6 again, as V6s (or V4s) of any brand are always tuned together in sequence, as they are inter-related. You then need to take it out and put her up on plane and then bring her back to idle quickly ... if she stalls ... yup, it needs a fine tune again. Also check your idle speed in gear.
These tests cannot be adequately done using muffs, they must be done IN the water. Anyone who tells you otherwise got lucky at best and is a fool at worst. I would also not attempt this without the factory OEM service manual. But if you had one, or access to one, they're easy to do yourself. Proper instruction and sequencing is the key here.
Myself? I would not trust a Clymer or Seloc "1 size fits all" :-| service manual ...
BTW, the Neutral-Start safety switch only prevents cranking while in gear - this is not your problem ... you most likely have a lean stall and I'm not surprised given how cables can form slack over the years, as well as motors may require a re-tune periodically.