EMM386 was emulating EMS using the 386 processor's ability to remap memory. EMS cards really provided it, independent of XMS memory. That is the better way, as EMM386 had to run the processor in Virtual 8086 (v86) mode. In v86 mode, closely related to protected mode, there were some limitations on what a program can do, which means that there's quite a few programs that can't run with EMM386 loaded. In DOSBox, this is no problem, not to mention it is more efficient. The problem for Mega-Em not running is because of one of the side effects of EMM386: it also provides a VCPI interface. This is what the error message notes (and the note below: "compliant with LIM EMS 4.0 and VCPI.". VCPI is an alternative (actually more like predecessor) of DPMI, allowing DOS/real mode programs to access certain features of protected mode. So, this has absolutely nothing to do with EMS. I seem to recall DOSBox at one point provided VCPI and DPMI hosts, but this may have been removed for a reason I'm not familiar with. DPMI is commonly provided by programs such as CWSDPMI.EXE. I'm not aware of any such program for VCPI, but that is the part you should be looking for (or, if you're feeling adventurous, creating).
BTW, the reason Mega-Em needed VCPI was that it could intercept programs that wrote to certain hardware ports so that it could get those values (meant for an MT-32), do its magic and send them on to the Gravis UltraSound. This interception was not possible (or at least feasible) in real mode, as far as I know, but it is possible in protected mode. That is what the VCPI was used for, not for its memory management.
Lastly, I see no reason to run Mega-Em inside DOSBox. DOSBox is quite capable of taking the real MIDI output meant for the MT-32 and passing it on to Windows. If you install the MT-32 emulator in Windows, you get better compatibility (more authentic sound and reliability) than with Mega-Em.
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