There is some evidence in the game code that PCjr is directly supported. The BIOS signatures of F000:C000=0x21 (Tandy) or F000:FFFE=0xFD (PCjr) will cause the WIBARM.JR program overlay to be loaded, however the machine ID of 0xFD will cause the game to use different keyboard scancodes than the Tandy.
The memory issue comes from how the allocation of memory to a .COM program is handled. All available conventional memory is normally allocated, however DOSBox is doing something different for machine=pcjr, perhaps because of the non-contiguous nature of the "protected" block at segment 0x1800. Instead of changing the memory layout, perhaps the way memory is allocated to programs could be made more compatible.
I worked around the memory issue by padding the size of the .COM file to 12KB, thereby forcing DOSBox to allocate more memory to it because of the larger program image. The game then starts up, however the keyboard does not respond normally, instead acting like the keys are mapped differently. I used the debugger to force the game to think it should use the same keyboard scancodes as the Tandy, and the game then appears to work OK. Note that the joystick can be used to get around the keyboard issue, although activating the joystick initially requires the keyboard.
Because the game reacts differently to the Tandy and PCjr BIOS signatures, I suspect the PCjr should work with the game, but is broken in DOSBox due to the memory allocation and scancodes issues. The memory issue seems straightforward to me, but the keyboard stuff could use further analysis. At any rate, PCjr support for the game is not that big of a deal, because AFAICT it looks and sounds identical to Tandy.