Throw away the vise? No. Throw away that tray that is making it hard to clamp things down. You didn't say if this is a floor stand DP or a smaller bench top model, but if bench top, the bench will catch things and if floor stand, get a broom.
I may get some heat for this, but if you are drilling smaller holes, like 1/16" or 1/8" I would clamp these small parts in a drill press style vise and hold that vise by hand. I would orient the vise screw to lean on or near the column just in case it does try to grab and spin. It won't get very far that way. If larger holes, you can drop some bolts through the vise's bolt slots and just put the nuts and some washers on loosely below the table to allow you freedom to locate the holes. The bolts will still keep it from getting too far out of control.
If the holes are larger than, say 3/8" or 1/2", then do bolt it down tight.
Parallels can help in positioning the part. Also, if you are drilling several holes, they are probably at one or two spacings from the sides of the part. Once you get the fixed vise jaw the right distance for one and it is bolted down tight, you can just slide the part on the parallels to the next hole(s) and re-tighten the vise.
Anyway, that's what I would do.
Last edited by Paul Alciatore; 01-26-2012 at 01:06 AM.
Make it fit.
You can't win and there is a penalty for trying!