The Gyroshtick is a very small model liike the simple G or Suitcase mini isn't it ?

Just as Tintrax described I also use plypropylene hinges and sideways trim is rarely required. I do find that I sometimes need side trim if the engine is mounted such that it puts the c of g off to one side.
Your over control descriptions do sound just like when I started out with my small Direct Control Gyro. Simple answer is to reduce the throws or ( ideally) use exponential on your transmitter if you have it. Start pretty heavy with up to about -40% and this should stop you over correcting.

I also fly really fast small flying wing models. Without expo they are sluggish with small throws at low speed or an oscillating nightmare when they get to about 200 if you increase the throws. Some folks either refrain from or don't understand exponential but I find it really useful especially on gyros.

I think my Simple G had about 6 degrees movement each side if I recall from days before I learnt to get to grips with gyros (or had expo)

Sean