I prefer rack pulls over deadlifts for bbing... Done on back day as the last exercise.
Or simply rotate deadlifts and squats from week to week. I can't do 2 big ass low-back involving lifts in the same week ... At least not for medium-high reps.
Also, if your low-back gets "inflamed" from those deads, you're likely either losing your arch or arching too hard (and thus weakening your hip drive)... I guess it's the former.
Check your technique...
Also, consider not doing them touch and go.
A lot of people seem to like it, I personally don't... I lift double-overhand and with straps on my high-rep sets (while training DC I used to do a 6-8 rep set and a 8-12 rep set or sometimes the other way around).
Usually have to readjust the straps between reps or reapply my grip after the first half of the set...
So try treating every rep like a single, make sure you're real tight, etc.
In bbing, with all lifts generally being done in the moderate or even high rep ranges and with practically every lift being a main lift/a lift you want to progress as fast as you can on, you really have to watch how many low-back involving lifts you do and when you do them in the week...
If I do rack pulls or deads on back day, I will do something like hacks, front squats (rarely as those involve the upper back quite a bit and that part is usually shot after back day, too), leg press etc for quads instead of back squats.
Also consider bent-over rows and such (I'd do them before deads, not after) as well as Stiff-legged or Romanian deadlifts for the hams... I only do one deadlift variation OR backsquats in a week..
Rev hypers and Glute-Hams are the exception, those are imo fine do to in the same week as deads/squats.