I have the same vise that Janger is trying to "fix", The problem with them is much more open clearance of the slide surfaces than a better quality vise & the fact that the threaded tightener bolt engages the sliding block under the jaw. The movable jaw will always tilt back a bit when it comes up tight to anything, even something gripped in the very bottom of the two jaws will tip it back.
making a cut perpendicular to the stationary jaw wont fix it, it just moves the same problem back the thickness of the cut.
I have studied mine a bit and the only way I can see to make the situation better is to run the movable jaw up to the solid one and tighten a bit, that will tilt the movable jaw back at the top of the opening the amount allowed by the slide slack, now measure the top gap with feeler gauges. The face of the slide must be cut at an appropriate angle to eliminate the "top gap" whenever it comes up tight. The slide slop & underneath tightener becomes a non issue.
my 2 cents worth at least LOL