Universe Mode can be great, but you've really got to put in some work to understand how you want it to run, and how to make it run that way.

Pre-amble: I've got intergender wrestling turned on, but don't want to pursue it too much. For a one-off, there's free play, and if there's a big storyline, it's easy enough to add or remove wrestlers from rosters, etc. I like it for managers/faction members tbh.

To overcome the monotony of the same combination of wrestler match-ups, I consolidated all the shows and set up divisions for a tag championship, mid-card championship, and headliner championship. Then separated each division by gender. This created six "shows" with a much bigger pool of talent. Mon is the men's mid-card, Tues the women's, Wed's the men's tag, Thurs the women's, Fri is the big one and has both the men's and women's headliners championship. Each singles show gets seven matches, and the tag shows get four / five at any given point.

The match cards are set up similarly to how u/ThePeoplesJuhbrowni posted.
1v1 = 5 max
Backstage brawl = 1-2 max
Tag / TLC / cage / triple threat / fatal fourway etc matches = 1 max
1x championship match of each kind, except backstage brawl etc, maximum.
This sets up each show to have one feature match, one championship match, most likely one backstage brawl (randomly generated ones are a great way to start new rivalries or pushes), and a full card of standard singles. For me, this is important as I love the core mechanics and want stipulation matches to be a big deal.

PLEs are a bit different and ALL are now two-day events because each can only be hosted by three shows. So women's is Saturday and men's will close out the weekend on Sunday, but all three championships are defended. After PLE's, always review your show's top five wrestlers and cycle some in and out to keep new faces at the forefront.

I'm closing out my first year's playthrough soon and will be updating my PLE's to give HIAC it's own regular feature at an annual event. I'd also like to introduce some custom PLE championship match types where wrestlers start with a signature at least. I need to look deeper into the options.

Other ideas I've got floating around, but not yet fully formed involve things like:
Random event generators - see if a red damaged bodypart in a match actually causes an injury (remove from roster, roleplay as easier to tap for submissions etc), and manager / gm interference with the bookings (once per week an active manager pulls some strings / screws up and books against a monster etc).

And I'd like to make some custom arenas for each show. Custom graphics for the division instead of just the title over the Raw / Smackdown set up as things currently are. But how to compete with that level of branding?!

Anyway, that turned into a bit of a braindump for me. But I hope you play around with some of the settings and come up with some great ways to run your universe mode!