Where to get vintage Movado Astronic serviced?

[PJ S]

As it’s a Movado, have you thought of contacting them directly or through the group, if necessary, MGI Luxury?
Failing that eliciting a remedy, then search for a local independent.
I don’t think LMVH has a policy in place to restrict parts access to accredited repairers/service centres only, so any competent watch repairer should have no problems changing the stem and checking the rest of the movement over for wear and servicing it.