I would suggest trying strips. Especially for the busier problems in the TSS with keeping track of guys in your pattern. Looking back (2 weeks removed from the academy) not one person in my graduating class used pad on local. Some of those who failed and used pad, I would say it wasn’t that they couldn’t work the traffic- it was them getting confused about who is who in the pattern.
Personally, I was in the same situation as yourself- early on. I used pad and it was manageable for the easy problems, but an instructor told me that he has yet to see a graduate use pad on local (not sure how true that is).
If you do go to strips, sort them bottom to top of order in your pattern are in line to land, touch&go, stop&go, or low approach. The ones that are full stop, turn them vertically once they’ve landed that way it’s less confusing with the others still in the pattern. Once they have landed write a big “E” “D” or “F” for the taxi way they”ve exited RWY 28L on, so you know where they are holding short of 28R and you don’t forget to cross them when you have a Chance.(most pad users get confused about who is who in between RWYs) This worked very well for me, especially when you get to problems 10-13 and you’ve got 3 guys doing T/Gs constantly thoughout the 45 minute problem, meanwhile challengers, gulf streams, and falcons calling up for a full stop. Lol. The last thing you want to lose track of is who is who in the pattern. Long story short- try strips.