Have never really understood while nets focus on batting, bowling, from time to time fielding but never umpiring and scoring.
Players have always been required to ‘take and end’ and score, and with all the courses available now I would be putting pretty much everyone that plays through one or both of the basic courses.
At nets I would have a umpire at each bowling end: ideally a trained one, but if not one that is likely to be required to umpire in a game. Obviously not one umpire all session, but rotate them.
Get batters and bowlers conditioned to them being there, bring some competition into the pactice.
You could even consider giving scorers the opportunity to practice by having the umpires calling dot, 1, 2, 4 , out LBW etc, then maybe captains and players could analyse these score sheets at the end of the session, players could keep copies and see how they improve (or not) over the net sessions.