There's no way to stabilize that design. It uses a coil compression spring to counterbalance the strings. It's basically a Bigsby B5/B7 with a slightly different casting and a higher price. You wouldn't be missing much, anyway. The "stabilizers" for the rear tension spring style bridges aren't all they're cracked up to be, either. They essentially just put a mild detent at the neutral point and hope you don't do anything that'll overcome it like a whole step or multi-string bend.
Maintaining tune
during and at the end of a bend isn't that big of a deal, and even hardtails don't do it. Fact is, from the moment you start to bend or stretch any string up to and including the point you stop bending/stretching, you're out of tune the whole time. The tension on different gauges and different constructions (wound vs. plain) changes at a different rate given the same amount of deflection, so bending two or more strings changes the frequency they vibrate at for a given length at a different rate.
This is why Fender's "synchronized tremolo" doesn't work, either. At least, not for keeping the instrument in tune. With
any vibrato bridge, if you intonate and tune the guitar
perfectly, then pull on or depress the vibrato bar to simultaneously sharpen or flat the whole string set
exactly one half-step, they'll no longer be in tune with each other. You won't go from open E to open F or open E#. You'll go to a dissonant mess. It would be difficult to bend a whole stringset with a hardtail, but you can unison bend several strings at once and the same thing will occur.
In practice, bending individual or small groups of strings while playing strings that aren't being bent doesn't happen very often, if for no other reason than there simply isn't room on the fretboard to do that. Bending or wavering a string puts the adjacent strings in harm's way so they can't ring. One of the things you have to learn to do is
prevent those strings from making any noise, as it's annoying and non-musical.
If you want to bend individual strings while leaving the others free to vibrate, there have been some solutions. Far and away the most popular is the "
B Bender", which is some fairly elaborate mechanical gimcrackery that lets you sharp the B string independently of the rest of them. Country players sometimes use them. I've also seen bridges with more than one lever to emulate the action of a pedal steel using your palm, but I can't find an example at the moment.
Anyway, long story short, you're probably worrying about nothing. Bends are more for the glissando sound effect than to reach any sustained playing position where tuning would come back into play. If you
are worried about it, rest assured that you're not alone. Others have worried about it, too. Then they got over it.