Moyes's brief was to get us safe into the new stadium. Mission accomplished.
I wouldn't begrudge him next season - and the chance to oversee the start of the rebuild - if the Friedkins do not have a top-tier manager, i.e., one we could not refuse, lined up. So, short of Carlo Ancelotti deciding he has unfinished business, I can live with Moyes for next season.
But, let's be realistic. Everything depends on what the club really aspires to. If next season is truly about stability, Moyes is surely our man. But if they fancy winning stuff and backing a manager big time, well, then the circumstances and criteria change. The old glass ceiling and "humble" knife to gunfight mentality will come back to bite us.
I think Moyes stays for a full season. If he manages to get us into, say, 8th place next season, he'll stay on again. It's like it was with Dyche - but on a higher rung of the ladder - once more. Dyche would still be here if he had moved us into 13th or 14th without any relegation worry (i.e., do what Moyes is doing now). He failed. He had to go. Moyes will have his chance to make his case next season, in all likelihood. Get us top half and he will stay on. Unless these Yanks have really big plans...