Here's what I'd do:
1. Automate as much as possible. Pulling the stamp machines, scales and other stuff that allowed people to self serve hurt them.
2. Go to three days a week delivery. One route on one day, a different route on the next. That cuts the number of miles driven in half, and would at most delay delivery by one day. MWF for one route, TTS for the other. Flip the days the next week.
3. About fifteen years ago, the USPS started doing rural route delivery. You can keep the post office and a few employees, but go back to PO Boxes in small towns. I know of guys who drive a couple of hours to cover something like ten houses.
4. Increase the rates for bulk mail - big time.
The biggest problem the USPS has is the unions (sounds like a broken record doesn’t it). They have three they have to deal with and the unions run the USPS with an iron hand. Management won’t cross them on anything. That is why they have twice as many people as they need and why thing never get done efficiently. I made a few enemies in both management and labor because I didn’t kowtow to their demands. I wasn’t a lifer I was a consultant and was there to do a job. I had a 3 year contract and cared less about what they union wanted. People weren’t happy, but we got things done.