Here’s a better pic of the copper band.

>> The "copper band" is an electrical "slip ring" (similar to a generator's commutator). The 2 slip rings are how electrical power gets into the rotor, so that its electromagnets can be energized. The amount of magnetism created by the rotor is directly related to the total amount of electrical power the alternator creates. 

So if the slip ring is loose, then the electrical connection is about to be broken... plunging the alternator output to zero. I'd say you found a big "problem waiting to happen" just in time. 

>> A charging system is a lot like a bank account. There are 2 ways to increase the account: 1) make more money, or 2) spend less money. Likewise, to keep the battery at a higher charge, you can 1) buy a high output alternator, or 2) use less power by converting your headlamp and tail lamp bulbs (and possibly others) to LED. 

Converting to a high output alternator sounds great, but you may also be forced to update your rectifier board to handle the higher current loads AND update your voltage regulator to a newer solid state unit. This because the alternator doesn't stand on its own.... it's part of an interrelated "charging system". So you need to think about the whole house, not just one brick.

And then there's the cost and time to install. A LED headlamp bulb costs about $25, LED tail lamp bulbs about $10 for both. You can install those in 10 minutes with nothing but a screwdriver.

>> I very highly suggest the modern solid state voltage regulator be installed first (with either choice) simply because a 40-50 year old mechanical regulator could be your entire issue from the beginning. 

Here's one that's plug compatible for most Airheads for a whopping $15 with free shipping !! CLICK HERE

Hope this gives you some good ideas.