Looks to me like you should mortise the rear jaw into the front of
the bench top, yet lowered the same measurement as the hight of that
lip, so the lip is flush to the bench top.

There would need to be additional spacer underneath to compensate
for the drop.

This way you could screw the rear (bench side) jaw cheek into the
front of the top, yet the screws going into both outsides of the iron of
the rear jaw, using countersinks for the screw heads.

Actually what I think you have is a natural end vise, the lip intended
to be the replacement of a sliding dog, not a front vise. That's a WIDE
one.

--
Alex - newbie_neander in woodworking
cravdraa_at-yahoo_dot-com
not my site: http://www.e-sword.net/