Question: Sterling Ax40 tremolo setup

So few months ago I bought a used Ax40 for 300 euros, I thought it was a pretty good deal, I haven’t seen these pretty much at all for sale in Finland.

So then I began to scroll this forum and I convinced myself to swap the original tremolo to a Gotoh GE1996T and I installed D-tuna on it. I also sanded the neck and oiled it with Tru-oil. I have never tried a real Music Man so I don’t know does the neck compare at all to the real deal but it feels good to me 🙂 I also ordered DiMarzio EP1111 switch for it, that will be the next upgrade..

But my question is: is it possible to set the tremolo flush and flat to the body? I can’t screw the pivot screws any lower or my strings will start to buzz. The front of the tremolo is now about 4 mm up from the body. It feels like this way the tremolo doesnt stay in tune like it should, unless I tighten the screws super tight and that’s not what I want.. :confused:

Thank you!!