Okay, time for what I hope is the wrap up report.
I installed a LiTime 140 ah, 150 amp BMS, Bluetooth battery this morning after fully charging it overnight. It came with a 52% state of charge, and didn't require any particular procedure to start topping it off. The LiTime Bluetooth app immediately started giving data, as it sat there charging. After I got the battery in, I installed a Progressive Dynamics lithium compatible converter, and reprogrammed my solar controller for lithium.
The original question was whether the jacks would work, and they do.
All of the other systems seem to work fine, with one odd exception. The LED lights in the trailer flicker when on battery alone. I went out and retightened all of the connections, and we'll just wait to see what happens on that.
Thanks to everyone who contributed to this discussion and to helping me work through this.