If that were mine, I'd just drill fresh holes through both the body and cap, (if you drilled them top and bottom, it'd scratch the OCD itch before it started

), and then tap the original body holes and pop a couple of brass grubscrews in, then peen them in place.
I'd concur, thats a simple repair which would work well, and restore the vise to serviceablity.
However........
If one wanted the finished job to to be 'very nearly correctly original', tho, it could be done.......don't ask me to do it, but if it was mine, and I wanted to be 'meticulous', here's a way.......
I'd first set the end cap up in the vertical mill, with one of the drilled holes aligned with the spindle, using a gage pin in a drill chuck.
Then, I'd drill and tap the end cap 1/8" NPT, and put in a cast-iron pipe plug, just a little past 'snug' with some red Loctite, after which I'd do the same for the drilled hole on the other side.
(cast-iron 1/8" pipe plugs were once common, and should be available, somewhere, with a bit of looking, even today......this might be an 'ask on machine hobbyists' boards on the internet item'....someone should have a couple of those in their old parts collection)
After the Loctite had set up, I'd cut off the protruding length of the pipe plugs, and file them flush with the curvature of the end cap, checking that the cap fit the back jaw casting easily.
Then, I'd counter-sink the drilled holes in the nut, and braze them up, using little carbon plugs to keep the braze up out of the threads. I'd file the brazed area flush with the curvature of the nut casting. Care must be taken to protect the existing threads in the nut whilst all this is done.
At this point, the 'end cap' and 'nut' parts are effectively as they were, at the stage in production before the holes for the pins were drilled.
I'd re-assemble the vise, with a suitable size of distance-piece (block of any scrap material) in the jaws, just enough to have the screw clear of the holes to be drilled, and tighten the screw, to be sure the nut was tensioned in place.
Drilling through the cast-iron plugs in the end cap, and the nut, is then obvious, with the drill guided by the existing holes in the back jaw casting.
At this point, one has the choice of refitting the original style of pin, or drilling the back jaw casting and the end-cap together, with the nut removed, to 'letter F' drill size, and tapping 5/16-18, to use the modified Allen set-screw (grub-screw) as mentioned earlier.
Too much work/trouble?.......yes, I rather suspected that you might read all that detail, 'glaze over' and lose interest......hard lines, theres 'no free lunch' in restoration work......... : )
cheers
Carla