A quick note about the Babicz. . . as of right now, I still think the price-performance king of the hill for aftermarket bridges is Gotoh 201 via Warmoth @ ~$30.00 .
but, because the Babicz is able to run significantly lower than the Gotoh, you might be able to run without a shim on the Babicz. . . or if already shimmed actually fit with the Babicz when the Gotoh will not go low enough without physically modding the saddles or reverting to the stock SX saddles which are not machined or coated as cleanly as the Gotoh ones. If that is the situation, the added cost of the Babicz outweighs the extra work and hassle of running a bridge that doesn't go low enough.
I venture to guess that ~50% of SX's even when shimmed will not be able to run the Gotoh without saddle mods. . . even with the neck shimmed. . . if set up for low-ish action.
Another note. . . while the stock saddles fit on the Gotoh, and the unit is functional, the saddle screws and the channels in the base plate do not line up absolutely perfect, so there is a little bit of wonkiness in that setup.