Not sure what your template looks like but i’m assuming your’e doing:
Upper, lower, rest, upper, lower, rest ,rest or something. With conditioning somewhere
Why not just swap?
Lower, Upper, Rest, Lower, Upper, Rest, Rest
Instead why don’t you do a more recoverable pull the day before DL?
For example, I tried doing press then Kroc rows when I was doing BBB. That was not optimal. So I did stuff like lat pull-downs or chest supported rows after press and moved Kroc rows to after bench. That worked absolutely fine.
So, if you’re doing BB rows or Kroc rows or any other pull that really taxes your whole body after press, move them to after bench and do less taxing pulls after press.
If ANY pulls after your press negatively impact your ability to DL the next day the problem may be eating too little, having a too high TM for your DL or having a seriously weak back.