Webkit's penchant for rounding decimals to whole numbers of pixels causes the sliding of sprites. Unfortunately, no amount of css can alter this behavior, rendering my above question impossible.
That said, there is still a way to use scaled sprites within webkit, though by necessity it uses javascript.
As you must ensure that the scaled sprite sizes are always in whole pixels, you should pick a sprite size ratio (such as 3:4) with as frequent (whole-number) multiples as possible, and then only update the displayed sprites' sizes when your scaling results in one of these. It isn't perfectly smooth, and definitely not passive, but it does allow for working, cross-browser scaling.
I've resized our sprites to 66*88, and using this I finally have scaling cards working. At the start of window resizing, javascript hides all of the sprites (cards, chips, etc.) and updates their sizes and locations upon completion. This effectively hides any jittering from the user during resizing, and greatly simplifies animation handling.