Just to follow up, I finally got my solar trickle charger setup today. I installed a 20w panel on the roof of my carport since it has good southern exposure and ran a ~25' length of 10ga wire to an inexpensive waterproof "Solperk" controller from Amazon. I then soldered up another 10" length of 10ga wire with an SAE connector. I have an SAE - Powerlet cable that I've been using to charge via fused Powerlet sockets that I install on every bike I've owned in the past couple of decades.
I have the controller set to charge at 14.2v until the battery is at 13.5v. At that point, the controller will monitor the battery voltage and float at 13.5v to keep the battery at 100%. When solar output drops below charging voltage (night/overcast), the controller will prevent the battery from discharging through the panel. I didn't get started on the project until late in the afternoon, so I only had about an hour of full sun once I got it all sorted out, but my multimeter says everything is functioning as intended.
I'll track the controller's performance on a spare "off-bike" battery for a week or so. I want to be sure everything is kosher before I hook it up to a bike. If it all works well, I'll buy a couple more controllers for the other bikes. The panel should put out enough juice to keep all three topped off since I tend to ride one bike (depending on my mood) and let the others sit sometimes for weeks/months at a time until I get bored and switch bikes.
Also, to answer one of the questions above, I did mean Li-Ion, not Li-Po. My kids and I have been playing with our RC trucks a lot lately and I've been charging a lot of Li-Po batteries for them, so I've had that on my brain. I didn't get a response from Shorai when I emailed them about the the batteries failed, so I just went back to Odyssey AGMs. I've always had good luck with them. The Shorai batteries that failed were used on my UTV and a boat. I only used the Shorai charger on them occasionally, but they still failed. The two good ones are on a tractor and another UTV and still seem fine.