I tried and failed at the soldering approach.
I suck at soldering and have little patience, and I destroyed that same $5 Amazon 4-pin XLR connector. Part of the issue was that I was trying to replicate what the stock connector has, where each wire was soldered to 2 of the pins, which, after seeing the pinout chart from Juiced, wasn't necessary.
Anyway, if others are soldering-adverse like me, the problem is easily solved with a $7 part from Luna (
https://lunacycle.com/xt60-male-to-barrel-male-plug-adapter/) if the Luna charger will be your only charger.
If you still want the stock charger as a backup, then you also need this $19 connector from Juiced (
https://www.juicedbikes.com/products/dc-connector-adaptor) so that you have a 4-pin XLR connector for each charger.
@Chuck E. Cheese is right, it's really not a hard soldering job at all and if I hadn't gotten impatient and destroyed the connector in the process (all my soldering sent too much heat through the pins and deformed some of the plastic casing) I would have had it working. But if you're the type of person like me where parting with $25 to let someone else worry about the problem sounds like a good idea, you can avoid the DIY route.