I am not a doctor. I am not a doctor. I am not a doctor.
However, my sports doctor always told me something along the lines of: (assuming you are healthy enough to do the activity at all) if you don't do the activity that is in question, how will you know if you are improving that activity?
In this case, if DLs are the issue, there is no way to know whether any rehab/healing is helping your DL issues, unless you do the DL. Now, this doesn't mean 1RMs! A reasonable recommendation is 50% intensity and you might go substantially less (for example, you said you tweaked your back on a "very light" weight ... you might go 50% of that very light weight). Build backup very gradually.
All the glute, 1-leg, etc. advice is very good. Blood flow is good. Don't underestimate the power of, say, bodyweight only good mornings, 1-leg RDLs, etc. Beware of doing too much volume as fatigue is a large factor in back injuries. I would be so bold as to say that your very light deadlift might have been the acute factor but that cumulative stress was the real culprit.
It is completely a matter of your own judgement, but a one day strain that feels good the next day is not always a reason to take off 3-4 weeks of (regularly scheduled) training. However, being prudent for the next several workouts makes a lot of sense.
As far as your programming goes, the amount of weight you are using and your training history will make a big difference in whether it is "too much" (back work) or not.