If you could only do one thing: either lab analysis of oil after each
change, or your own visual examination of oil and filter after each
change, which would you do?

I'd quit, on the basis that the universe had just become too perverse in
contriving such a situation.

Visual inspection will catch some problems, oil analysis will catch
others. The two sets of problems have some things in common, but a lot of
things will only appear in one or the other set.