Not
quite sure what you mean by "
too strong for the stock Trailwings". If your bike is "all over the place", at speed, I kinda doubt that it's completely due to the `Wings. True, they're not as sure-footed as street tires, especially for the first few hundred miles, or so. Tracking does improve with wear. If you want dualsport capability, they're as good as it gets. After 21,000 miles of use, I've relegated them to a second set of rims...that will probably never see the bike again. However, my reasons are probably different from what you expect.
If you're accustomed to fullsize bikes, a modded CT70 is going to feel comparatively twitchy, for a time. Low mass, small-diameter tires, and short wheelbase have that effect...inherently. For your own peace of mind, I suggest figuring out how much of the twitchiness is actual, mechanical, instability and how much is personal perception. Any mechanical issues (loose chassis/suspension pieces, swingarm bushings, etc) should be corrected, obviously. That K1 fork should be pretty good, if everything is tight and you've done the oil-tuning thing. A loose axle, or headset bearings, however, can make it feel like rubber. If anything has excessive, unwanted, lateral movement, it's more likely to be swingarm-related.
IMHO, these bikes feel like they're moving along at ~1.5-2.0x actual speed, compared to anything full-sized. That's part of the fun. Mastering a new (sub)set of riding skills, specific to these diminutive machines, takes time. It took me a few thousand miles to really settle-in...to the point where riding one of these little bikes feels like second nature. (Of course, I also took a 20-year hiatus from motorcycles, which didn't help.) I doubt that this is unique to me.
At this late date, I don't find the venerable `Wings all that bad, really. Their light weight is actually quite a benefit. Fastest "Banzai blast" on my daily rider was on them...67mph and stability was not an issue. They don't even corner badly. Ironically, that is the primary reason for switching to road tires. My machine fairly begs for a good workout, including peg-scraping lean angles, through the twisties, and that's where knobbies are fatally flawed. Reach that last row of tread blocks and the bike would washout faster than a rider could think the words "oh shit!" The other two reasons are noise and short tread life. That buzzing noise sometimes gets on my last nerve. And, by 3500 miles, the rear tread has worn enough that it noticeably affects gearing.
If you want to retain the stock profile of the bike, you're limited to ~18" tall tires. The absolute limit, with stock suspension pieces, is ~19.5" and you'll lose some chain adjustment range at that. IMO, they look a little clownishly oversized but, to each his own. Any taller and you'll risk disaster should the suspension ever bottom-out. You'll also need to address gearing, if you change tire circumference more than 2-3%; speedo input, and with it the odometer accuracy, are also affected. Personally, I'm not a fan of 12-inchers on these bikes. The shorter sidewalls will stiffen an already firm ride quality and offer less rim protection. Again, it's your call to make. Don't know about available sizes in 12" flavor. Most of the 10" offerings are metric, few are sold as 4.00-10. Bridgestone used to offer ML16/ML17 as a front & rear, directional tread, combo...in 4.00-10. The front was unceremoniously deleted at the end of 2015 (those bastages:yell
Not sure if the rear can be used for both. Actual size of a Trailwing is 105/90-10. That's an important concept...the difference between nominal (shown on the sidewall) and actual size; it varies wildly, with all manufacturers. You've been warned. Pirelli, Metzeller, Avon, Continental, Cheng Shin and others offer a number of 10-inch road tires. The best of them, bar none, is the Heidenau K61. Check the current catalog, available sizes change from time-to-time. Their 110/80-10 was the closest to OEM size...both section width and height.
