I'd go for a much larger battery than that dude, especially for that price! 1.2ah probably isn't going to last a long time running speakers loud enough to be heard over that 2 stroke. It'll run even less time if you put a lighting setup on the same battery (and why wouldn't you, do you really wanna charge 2 or more batteries every time you get home?) And on top of that if you DO run these SLA batteries down below 10v you can cause permanent damage to them. You want to always be sure that you're going to have power to spare and that charging isn't going to be a pain in the butt as its best to recharge them asap after use.
With my lighting system I used 16ga automotive wire and a ton of parts from that electric scooters part site. There was no soldering involved just some cutting, stripping and crimping. I used a bunch of insulated tab terminal connectors to hook up all my components. You'll have to be sure to get a multimeter too just to make sure you're getting your polarity correct or you will destroy your electronics or start a fire. Always place a fuse as close to the hot terminal (+) as possible just in case something shorts out.
Maybe you could get a pannier bag setup built for Ebikes. some of them have two side bags and a top bag meant for batteries/storage. You would just have to find a way to mount a rack on the stingray, the rack would probably require some modification since the rear wheel is so small on them and the seat is further back than common bicycles.
I like the idea about the car stereo much more than the boombox however you would probably have to keep it as one solid unit. Which means if you wanted to put it on your dashboard it would be incredibly clunky. A boombox dial would be just as difficult to incorporate into a dashboard. I've taken them apart before and it would basically involve re-engineering the whole dial mechanism and syncing it to the correct frequency again In either case you'd have tons of wires mounting anything up on the handlebars like that. I would think it would also be a ton harder to waterproof exposed like that rather than secured and under the flap of a bag. The push preset ones would be perfect, I'm pretty sure modern LCD radios suck down more juice too which is not favorable on a machine with no alternator (yet)
If you want I can assemble a parts list off that site for you. I can vouch for them, I have my electronics box almost complete (just have to mount it on the bike, hook up the brake switches and headlight) and every component works perfectly. I think their stuff is chinese but what isn't these days... In either case I didn't receive anything that was overly flimsy, defective or even rough around the edges.