Cryptic, I don't know whether I said it above or if it was in the reply that disappeared. but to go along with what Occupant said about using a "deadblow hammer", make sure you have a deadblow. I have watched people use small ball piens or a round piece of brass to set their parts in a vise. A hard hammer will bounce your piece off of your parallels every time. A rubber tipped deadblow will set the piece firmly against the parallels.
With tall jaws, you will have a little more of a problem doing it because a tall jaw will propose two problems. One....the jaw itself may flex some. Some may argue that steel won't flex. And I'll argue that it will. Plus the taller the jaw, the more chance of it raising the moveable jaw block off of the bed where it rides. A small jaw can do it also, but a taller jaw will magnify the problem.
Also in my missing reply, I asked you to measure your vise jaw bolt pattern. I may have a set of short jaws that you can use. On mine, the bolt pattern is made for a Kurt vise. The bolt holes are 11/16" up and 3 7/8" center to center. So let me know what you have and I may be able to hook you up.
If you get a chance sometime, order you some 1" x 2" aluminum. It comes in very handy for making special jaws, and it's cheap enough that you can keep a couple sets of jaw blanks around for making a set. At work, anytime I made a set of custom aluminum jaws, I would also machine up an extra set of blanks. I had around six pair on hand at all times.
Also, if you do pull your mill out of the corner, you still want to have some metal against the wall behind it to keep chips from hitting the wall. If you use oil when milling, you really don't want oily chips hitting the wall. Or if you don's want to mount metal to the wall, take some Electrical Conduit and four cheap casters and a tarp and fab up a 4'x8' shield that you can roll behind the mill when machining. Then when you are not using it, just roll it away somewhere. Another idea would be if you could find an old movie projector screen that you could mount on the wall, pull it down when machining, then roll it back up when done.