I would consider a semi rigid back-pack which you could mount on the back of the seat behind you. Better than a "trunk" box since you can take it off and put it on your back should you want to take a short hike or take all your stuff into the motel room. It is "soft" enough that it can also serve as a back rest if positioned properly.
A second trick is to use Fedex/UPS. Send all the clothes and stuff you'll want while visiting your friend to a nearby address on the way. Once you are south enough, ship the cold weather gear to an appropriate address that is on your return trip's route in case you need it then. On the way home, when you get to the address where you sent all your cold weather gear, ship all your beach clothes and vacation stuff (and anything else you now won't need) home.
The money you save on gas by not pushing all the weight all the way (not to mention reduced wear on the bike) will pay a good portion of the shipping cost. And avoiding a breakdown due to overloading is hard to put a dollar value to, especially if you avoid it
. If you get home without a breakdown, assume you saved a bundle
and incorporate an appropriate high dollar amount saved into the story you will tell.
My friend who did over 35,000 kms last year on a 30 yr old BMW 1000, carries a small solar charger which can bring his battery back and charge up a cell phone etc. Mind you, that's for on roads in Alaska and Yukon where one can wait all day for a single vehicle with jumper cables to come along and help.