Thanks. I found some workarounds. I'll post in case anyone else is in hell with the Elecom M-HT1DRBK wireless trackball mouse:
There are 3 options for programming the Elecom Trackball: BTT, Elecom's Mouse Assistant or both
If BTT only, BTT sees 7 of the 10 available buttons. However, for 2 of them need you to hold down a modifier key to override the key for remap. This leaves only 5 of 10 buttons for remapping with one-handed operation.
If Elecom only, all 10 buttons are available, but remapping is global not app specific, and there are limitations.
If both, all 10 buttons can be mapped in Elecom mouse assistant, and BTT can override two buttons and make them customizable per app. Those two are scroll wheel Tilt Left and Tilt Right.
There you go, and here's the page for the Elecom "mouse assistant"