so here's my question how long could the system of absolute monarchy centered around the court at the Château de Versailles, the system of the Monarchy set up by Louis XIV and maintained by Louis XV and Louis XVI till 5 October 1789, last?
It couldn't, and actually didn't lasted after Louis XIV's death.
Louis XIV system was absolutist in the strictest meaning of the word : meaning all ministeries weren't responsibles, the king was. Not to say the kingdom was centralised, the shitload of different, overlapping and rivaling juristiction was quite the contrary, it's not because absolutism was the political model used that it was omnipresent (such as it's not because you're living in a democracy that every aspect of your life is based on it)
But the point was the king ruled alone, was the sole responsible of policies but could give a power of delegation to his councilors (usually not old nobles, but recently annoblished persons, something that was quite new in France) and people he delegated power were responsible before him only.
It's the system that asked both a skilled ruler and the minorisation of ambitious nobility (as in, let's make then inhabit Versailles if they want anything from me, and once there, make them my puppets) that had no other choice than remain provincialist in a time where Versailles was the power, or to be under scrutiny.
Attempts as polysynody backfired hilarously, but it was the beggining of the end of Louis XIV personal system, the remains being kept half because nobody had a better idea, half because of the prestige of it, eventually fossilizing it while being twisted (as the idea itself of absolutism changed over time.
Basically, you'd need someone else than Louis XV. Anyone else. Pick the first guy you'd found and it would be statistically better.
(Okay, okay, i'm exxagerating it a bit)
He simply got absolutism wrong. As in "I'm always right" rather than "I have to be always right" that was more on Louis XIV, hence he didn't really minded paying attention to councils or ministers, and did as he wanted. Add that a character being interested only at times with administration and politics...
Even Philippe d'Orléans would have made a better king, or maybe one of Louis XIV's bastards (that he legitimized, and tried to make heirs, but the testimony was broken).
in OTL its extreme absolutism and centralism around the person of monarchy was very out of step with the rest of Europe,
Prussia and Spain would disagree. Absolutism was relativly "fashionable" as monarchism was during the Roman principate, as in the idea of a strong man being able to overthrow bureaucracy, oppresive middle-men, and to tie a real personal link with his subjects.
but could it have lasted longer with a stronger or smarter King then OTL's Louis XVI or was he doomed from the start no matter what he did?
I don't think it could have lasted as such : reforms were necessary, as they were during Henri IV or Louis XIII's reigns, rather than putting all of it in a relic chest and get on with it.
Maybe an earlier death of Louis XIV would be a good thing, his end of reign was put in the shadow of his better years, and that really didn't helped to a more dynamic change.