. I would split your question into two:
- have the service performed by LVMH or by independent; and
- when to service.
1. It is said that El Primero, due to its high frequency, requires some parts to be lubricated by a dry lubricant, molybdene bisulfide applied by vaporisation, instead of ordinary oiling. Therefore, I would be very careful to whom to hand my EP over for service. (NB that El Primero adjusted for Rolex beats at 28,8 vph thus permitting traditional oiling, therefore even Rolex skilled watchmakers may not be a good choice).
2. I have been facing a similar dilemma recently since the older of my EPs started to slow down in rate when the chrono is actuated while without chrono, decrease of amplitude and rate in vertical positions can still be considered acceptable. To be on the safe side, I would tend not to wait any longer and send her to spa... I.e. I consider to have my watches serviced when they change their typical behaviour, rather then by servicing in fixed intervals. For reasons highlighted by Art, I will appreciate any comments on this approach.
petr

As to the first question, should you service it, unless the watch is running slow and giving signs of being in need of lubrication, I wouldn't service it.
Regarding trusting your local Zenith watchmaker, why not? That he's local is advantage as opposed the sending it cross country and then trying to solve issues over the phone. If he's Zenith authorized, presumably he's as trustworthy as any other Zenith watchmaker elsewhere.