only new york state certified shops can issue n.y. inspections.
if all you need is an oil change and a safety inspection,any local dealer should be safe to deal with.
i wouldnt even wait for a far out date just to get a loaner. schedule an appointment and wait in the lounge, it shouldnt be no longer then an hour.
the loaner route is 2 trips to dealership,much more time lost.
i live in n.y. have my car serviced in n.j., its only 20 minutes from my home.
a couple of weeks ago i went to bmw dealer for oil change.
this week i will go to my neighborhood garage for n.y. safety inspection.....in and out 10 minutes,cost $10.00