I think the best bet, if you come across a cable that’s a pig to replace, is to take the carbs off, replace the cable, (at the carb end), then the carbs. Then feed the cable back to the throttle. If you use a ‘messenger’, it’s easier.
Keep the Airbox. Heat the rubbers up with a hair dryer or boiling water. There used to be some kind of concoction you steeped the rubbers in overnight, and they were quite supple in the morning. Buggered if I can remember what it was. Someone on here might?
Cut & shut stem is perfectly ok if done by a competent welder. Cut it, turn a tight enough slug, chamfer both ends of the stem. Fit the assembly to the frame, and tap the top of the stem until you get the length you require. MARK the stem before you give it to the welder, and explain what the marks are for. Dress the stem on completion. Done!
And so it does! I can’t see why Suzuki would put a bearing in, with no means of getting it out undamaged. If there’s definitely no lip, weld a ring around the race, and it’ll shrink. To avoid the same problem in the future, get your Dremel and grind a couple or slots (or three) equidistant around the inside of the neck. This’ll enable you to get a small drift/screwdriver around the outer, to knock it oot!
Get yourself one of these. I fucked about with punches, drifts & long screwdrivers for hours. Everything slips off the lip of the bearing! When I got this, I had my outer bearings out before before the postman was out of the street! Well worth the money!