You can disconnect the encoder motor and shift it manually. I know they make a tool for that, but I believe it can be done by pliers or similar. Here's some info:
https://hummer4x4offroad.com/forum/...abs-will-block-your-tcase-from-shifting.9261/
When you press the buttons on the 4wd shift control, do they flash light they are trying to make a change?
But, it's quite possible the issues are linked. The brakes may be the key. First, I would verify that all of the ABS sensors are intact and are not disconnected or have any broken wires. As you can see in the above thread maybe one is bad and it might take an advanced diagnostic tool to figure out which one. Next, I would try bleeding the brakes. Start with the rear and do all four. Put a quart of DOT3 through there. Note that the engine must be on in the H3 to bleed the brakes. Bleeding them will remove any air in the lines, or deteriorated fluid. You might also find a defective caliper or other issue at one of the corners that's causing the ABS issue. I would pull off each caliper one by one and inspect them. Since you're in PA rust could be an issue, or deteriorated rubber components.
Do not step on the brake pedal with the calipers unbolted from the truck. You can overextend the pistons and cause ABS issues. Trust me on this one.
Of course it could be two different issues where there's a brake issue and maybe a worn shift fork in the transfer case. Have you changed the fluid in the transfer case? If so, what color was it - red, blackish, bright silver? Any chunks or excessive shavings?