I would add more volume to the main lifts. Instead of working up to 1 heavy set of 3-5, I would bump it up to 3 sets. Maybe aim for 3 sets of 5, and when you get all 3 sets of 5, move up in weight.
If you're eating to gain weight, you can handle the extra volume and it will carry over. Assistance work is great, but isn't a replacement for the core lifts. I think until you are strong enough to get a training effect from 1 heavy set, adding in more volume in the form of more sets is an easy fix.
Check out 'mobilitywod.com' for mobility/stretching/stuff. It is pretty varied and if you do it every day, eventually you will fix your issues and find trouble spots. Also, I'd post vids to make sure your form is ok.
I'd add deloads in too, if you aren't doing it already. If your back issues are the result of cumulative fatigue they should start to fade by the end of the week.