I switched from SL 5x5s to 5/3/1 recently, just before I hit intermediate numbers for my BW, after I'd hit some pretty big plateaus on my 5x5s. I'm no expert so I can't offer advice, but I will share my experience in the hope that it's useful:
1) I followed Wendler's suggestion and set my TMs initially to 90% of my 1 RMs. I ended up with several AMRAP days north of 8 reps, especially on the 5/5/5+ days. The problem actually got worse, in my 2nd cycle I had a Squat day where I got to 14 reps and a Deadlift day where I got to 12. I can't say if that's normal, but my experience is congruent with your own.
2) I did 5/3/1 vanilla out of the box for my first cycle and found it was too little volume. For both Bench and Squat, my weekly volume went way down only doing the prescribed 5/3/1 work sets compared to the volume I was doing on 5x5s. If you haven't read 'Beyond 5/3/1', I would highly recommended it, as Wendler gives you several programming options which I think you might consider to address any concerns of 5/3/1 being too easy or too little volume after switching from 5x5s. I changed two things to get my volume back to where it was:
Added BBB 5x10s at 50% TM for Squat and Bench. (Still debating if I do this next cycle for OHP and/or DL.)
Added 'Pyramid' drop sets to all 4 days. So after the AMRAP / PR set, I drop back and repeat the 2nd and 1st sets again, if I feel good I do AMRAP again on the very last set.
3) The two changes above brought my weekly volume back up to levels comparable with what I was doing when I switched off SL. I'll also likely start adding Joker sets to my programming on days I feel good, but I'm waiting until next cycle as I want to progress slow and be sure I'm recovering effectively from the BBB volume. (Those 5x10s feel easy, and then I get crushed with DOMS the next day!)
4) Nonetheless, I'm super happy switching and in my experience 5/3/1 was essential to breaking through the plateau I was having on SL. Two things I think really benefitted me about the switch:
I'm enjoying the program much more because every day in the gym is an opportunity to PR on the AMRAP set. On SL I was feeling burned out on the cycle of fail, fail, fail, deload.
I also think I'm benefiting substantially from moving more volume at lower weights, the lower weight work sets and BBB sets are great for really focussing on form and depth/ROM.