If you want to make this with elevons one way to couple the aileron and elevator function is to make the elevons taper in all the way to a wider center width. Make them about twice as wide at the center as they are now. Connect the servo at the mid point to gain as much from stiffness as practical. And using C grain or glassing the elevons as mentioned would not be all that bad an idea.

You also want to use a medium long arm on the servo and equivalently long control horns. Then use the outer holes or only one or two holes in from the outer to achieve your max deflection angles. This reduces the effect of any slop in the system.

The idea of using the wider elevons with the strong taper to the tips is to avoid the ailerons becomeing too sensitive while still not having enough elevator authourity. The wider center will ensure that you get the elevator control you require.

You didn't say how much aileron throw you're currently using. If you reduced it in an attempt to reduce the flutter issue then you may just not be using enough deflection. More info on this regard in terms of amount of deflection either as angular degrees or X up and down over Y width would assist.