Other strings going flat when you bend one of them is very normal with FR ... I don't think that Extra springs or anything will solve the problem unless you find a way to block the bridge (but it won't be a tremolo anymore , you should have got a fixed bridge guitar instead).

Anyway , what I do to overcome the problem is bending the other string slightly and the string that should be bended a little more ... Sounds hard and complicated but it's not .

i.e. a unison bend like this

e----
b-7--
g-9b-

What I'd do here is bending the 9th a little more and slightly bend the 7th , so that you get them sound normaly in tune.