Hey,
I am in the same boat as you (sort of) I have been reviewing an larger displacement engine swap vs. BBK. Before you do any engine work, you have some forethought to give other parts....
Brakes. The brakes on the grom are not terrible, however, they are fairly mushy. At the very least, SS brake lines help tremendously. In addition, a different caliper or rotor, or both can help as well. Especially in the front. I wouldn't be too worried about the rear, given the tires.
Tires. Replace. They suck. End of story.
SUSPENSION. Unless your 110-125 the suspension is crap. If you going to bee adding weight with engine parts...SUSPENSION. Stiffer spring in the rear at the very least. But if you are thinking about big bore, don't cheap out. These parts are your platform to build on. Full shock with adjustable damping on the rear, and rebuild the front. Springs and valving. Don't just add higher viscosity oil.
Okay, if you decide to go big bore. Grab a pipe, CAM, Intake and ECU. Start there. Then grab your big bore kit and switch to synthetic oil!
If you are going to go engine swap, which as I said am also still on the fence about, lots to think about. People thinking im ludicrous for putting a 250 in it. I don't want to pee in your cheerios, as I don't want anyone to say the same to me, but a 600 engine is dumb. It's wide. Think about where your legs would go, where your shifter goes, where your rear brakes go. Your on 12 inch wheels. That swap would require several larger radiators mounted. Lots of fab work for a massive under frame. You would lose the grom in that, I don't think the engine would fit between the side panels.
Think thumper...I want to put in a 250r engine from a CBR250. a crf450 engine has been done. If you want to go nuts, look for a KTM 690 engine. You would lost all ground clearance.
Think about fuel pressure, fuel consumption, wiring harness, electrics, ignition. All this stuff needs a place to live. I say you look at the 250r swap and I will do it when you complete it. I am about to wuss out on my build and go with Brians 170 kit. I don't want to weld on my frame yet. I am thinking I will by a third and butcher that one when the first two are paid off.....
Lot's to think about man. If you have a complete bike, and all the parts, that puts you so close. Just strip both parts and mock it all up, see what you can do. I think you can do it, just know the work it's going to take.!!!!!
Enjoy!