13.8 VDC should be fine and the battery should charge. Ride the bike some and get it charged via the bike's system and then try and start on a cold morning. Also, keep in mind that the oil you use in summer may not work so good in the winter... gets thickkkkkk on 30 degree mornings. Go to a bit lighter oil in mid-winter. I have pretty good luck running 15W40 year round. This in case you use 20W50 in the summer as many do in hot climes. As far as the coil re-power mod, just take your time as the job will only be as good as you do the details... no cold solder joints and use heat shrink and then wrap with electrical tape to prevent chafing (and shorts down the road). Let me know if you need any questions answered.
wiredgeorge Motorcycle Carburetors
Mico TX www.wgcarbs.com
Too many bikes to list!
After riding to and from work yesterday, about 60 miles round trip, I put the tender on the battery and the green light came on immediately. First time that's happened so all looks good in the charging system.