Another update...the 360 is still alive and kicking - as I said before, I've been riding the heck out of it.
Updates I've made have been minor, but have helped rideability a great deal. I finally replaced the chain (39 years, is that all I get out of the original one?!?!?) and sprockets, and my God is the bike so much smoother! I picked up an eBay bundle of JT sprockets (stock tooth count) and an RK 350 chain from seller "lytleracinggroup" for about $85, and other than discovering that three of the four nuts holding the rear sprocket on were less than hand tight
the install (with loc-tite!!!) went fine. I did have to cut a couple of links off the chain they sent me, as it was a 100 link chain, a bit too long. Hello angle grinder with a cut off disk.
I also replaced both the clutch and brake levers with replicas (complete with that fancy plastic dipped end), to try to get the "flop" out of the levers. This helped the clutch, but the brake lever was still funky. It turns out I was missing the bushing that's supposed to be the disengaged stop for the lever. I made a new one out of some vinyl tubing, a cut down nail, and some sheet metal to hold it in place, and greased the heck out of it. No more floppy lever. I also lubed the control cables while I was at it, which helped smooth up the clutch action.
The mufflers were also packed with a couple "pads" of stainless steel scrubbers to reduce noise a bit. It's helped some, I don't feel I need earplugs riding around town.
Finally, the last "mod" I made was switching to 93 octane gas. That took most of the midrange herky-jerkyeness out of the thing. It was just a random "let's try this" thing after a long fast ride out into the country. I had to diddle with the idle a bit, and ended up backing off the idle fuel screws from 1.5 to 1 turns out, but it made a clear difference. I have to use the choke to start the bike on cooler days now too, interesting as I've never needed the choke to start the bike before.
I spoke with my Dad's best friend, as he owned a new CB360 "back in the day," and his theory was "regular" gas back then was low lead 91-95 octane. The high octane he ran in his modified big block Corvette was 100-102 octane. He ended up trading in his 360 on a Norton Commando 750, so I'm not sure how much we can trust him ;D
I also pulled the rear "hoop" off the frame and beat the hell out of one of the stock tail light mounts to straighten it back out. This, of course, let to me repainting it and the tail light bracket, as well as the fender mount clamp, first with etching primer and then with Rustoleum Satin Black. I find that color black matches the stock Honda frame paint pretty well.
I also polished the fender with steel wool and WD40 and painted the inside of it with Rustoleum Rusty Metal primer after wire brushing off as much of the muck as I could. I then hit it with a couple coats of rubberized undercoating spray. Turned out pretty well, I think!
The quest to scrub the chicken strips off the tires continues, but I keep bottoming out the pegs and exhaust. I think these Shinkos offer a little better cornering grip than stock issue for 1976.
What's left to do on it (other than a full teardown and repaint, which may never happen while I own the bike, as it's only original once) is to fit a steering damper to the front and to replace the shift lever with an original style one.
The steering gets a little floaty at times. Turns out that after I cleaned and repacked the steering bearings, the steering is much smoother. The old bearing grease was acting like the world's worst friction damper! I picked up a Suzuki damper off a GSX-R or Busa or something on eBay, but need to get a fork tube clamp mount, as the lower triple's stock mount boss is too small for the diameter of the Suzuki's mounting bolt. Mounting ideas are welcome!
If anyone has a goodish stock lever to replace my obviously wrong and bent to shit one, I would be glad to send you $$$ for it. At some point the welds on the one I have are going to fail if I keep having to bend it.