Hey, Bill,
A fellow by the name of Wayne Huff over on the Thumpertalk Forum, vintage sub-forum has done a no-battery conversion of the early Honda SL100. This would be virtually identical to what you'd want to do to your 350. Other than the 6-volt / 12-volt differences and 1-cyl vs. 2-cyl, I think it would work perfectly.
Here's his website where you can find a very good write-up on how to do it.
http://waynescyclegarage.mysite.com/A couple guys over there have done it per his instructions, and all rave about it.
Good luck.
*edit* - here's Wayne's write-up from a thread he posted on the subject on The XL Forums on oldrice.com:
SL 100 battery free!!
Heres how I did it which is easily reversable if you don't like it which I can't imagine.
This is for racers or bikes that need no lights and is not a cure for tuning problems etc.
You will need an AC coil (where the plug wire comes from). I used one from an old Honda Express which had the condensor (capacitor) built on. Just about any coil from most of the two stroke magneto powered bikes will do if you can mount it.You will need a Honda rotor puller. Do not try to remove the rotor without it, It is basically just a short bolt but would be a good investment(cheap) and will remove just about every Honda rotor out there.
STEP ONE: Start with a well tuned SL , the point gap and timing should be in specs.If not your reference points will be wrong.
STEP TWO: Lock the advance to full. I simply removed the bolt/washer that secures the point cam and advance mechanism,I found the perfect washer that just fit over the camshaft end and was just thick enough to bind the point cam in a fixed position.(full advance).when I replaced the bolt & washer.There may be many ways to lock the advance but this was so easy.
STEP THREE: Remove the rotor and woodruff key. Set the key aside as you will not need it. Clean the rotor and crank taper with contact cleaner etc to remove all oil and residue so the rotor will not slip.Turn the engine over to the point the contacts just start to open (fire).Install the rotor with the magnets aligned with the windings on the stator. If the holes instead of magnets are lined up with the coils you will have no spark when you need it.Replace the rotor bolt and tighten to normal torque. It should not slip as the taper is the main thing keeping it in place and not the key.Scribe your new fire and TDC mark on your rotor for future tune ups.
STEP FOUR: Unplug the harness coming from the stator.It should have 4 wires, one is for the neutral light switch. Remove that one to get it out of the way.That leaves three, you will use two.The pink wire goes to your newly installed AC coil.The yellow wire goes to ground to complete the circuit. The other one is not used at this time.
STEP FIVE: Wire you up a simple kill button or switch, remove the rectifier, uneeded fuse and excess crap and enjoy the simplicity.
I have had time to test this and it works great, the bike should start easy as ever and maybe even run better.Mine hits a little harder from the bottom(the advanced timing). Play with your timing some if you want just remember the magnets have to line up with the windings when it fires.I like things as simple as possible and I don't have to worry about keeping a battery charged as well as the weight and corrosive propertys of a box of lead and acid!
Your bike will crank and run with the original DC coil but do not be tempted to ride it! It can cause major engine damage like holes in pistons.The AC coil is key to this mod.Now what do I do with all that extra room where the batt and rectifier went? I'll think of something.
Thanks for all the help, This works really well and should give you no problems.
DirtHippie, wayne huff
I will remove the extra windings in the stator soon and will update that procedure.