I think Belichick wants Shula's record, so he will remain a coach for a few more years somewhere else if not here
I think you're right, but it's not really his decision to make. He started the season needing, what, 18 wins to break the record? After a whole horrible season, he needs 14. No owner is going to keep him on as head coach for another 2-3 years - at minimum - just so he can eek out a personal record that is largely meaningless to the organisation.
I think a lot of owners outside of New England would hire him. For instance, the Chargers would seem to be an okay fit for both sides. The question is, will Bill coach without 1) personnel control and 2) his staff of nepotism and friendship hires?
Maybe, but the fundamental question remains: why? I guess if you're under the assumption that he hasn't lost his fastball it's a reasonable move, but if you think he's still 'the' Bill B. then surely you'd be onboard with making him the GM - even if it's a de facto role - as well?
The dude does not look like a great head coach without a great team, which is fine, but what existing good team is looking to bring in that kind of baggage? I'm sure the teams are out there - Chargers, as you mention - but I'm just not convinced a front office is really making the best choice to bring him in, compared to the mythology.