I think what I see here is someone who needs the bike to offer some excitement. I totally get this and divide them into bikes that give you a woody and everything else.
To me, a 650 strom does not offer a woody. I view it as a tool,when I use it the bike is about where it takes me, in this case rough backroads, dirt roads and such.
Now,to contrast I also have a 1050 Tiger which can fulfill much of this and I see as a wood producer. Power is a part of it but so is better attention to detail and a nicer finish,just plain more bike.
I think one never knows what will give wood but it sounds like the 650 aint it. Maybe check out similar rides like an 800 Tiger or a Versys, maybe even a multistrada.
'14 HD FLHR
'01 HD FXD
'09 HD XR1200
'79 BMW R100