Here is what I do for resawing short pieces on the bandsaw, because my vise jaws end about 1.5" from where the band runs: cut a couple of 'extender pieces' of 1/2" or thicker mild steel (or cold drawn C1018 would be nice as well), maybe 12" to 16" long. Lay them inside the vise as per normal, with the ends almost touching the blade band. Cut a precision spacer to match the stock width of the pieces you wish to resaw. Place this spacer at the far end, between your two extenders. Then, place your stock piece in position under the band. Tighten the vise. This is all easily done if you have 4 hands
Now you said you had a lot of these to do, so maybe it would make sense to 'fancy up' the extender bars. Primary concern is getting the part sitting square on the saw bed, so to facilitate this, mill a shoulder at the working end of the extender bars, creating an inset to nest the stock in. If you wish to increase the grip, I'd suggest using a threadmill to mill a fine serration in the wall of this nest.
You could also use a screw jack at the outer end of the extender bars. This will permit you to make fine adjustments of the seperation of the extender bars, if your stock width is poorly defined.
First you get good, then you get fast. Then grouchiness sets in.
(Note: The opinions expressed in this post are my own and are not necessarily those of CNCzone and its management)