I think a lot depends upon exactly what you want. Specifically, do you
want HW compatibility with the Exec Mode instructions, or is it
sufficient that the emulator provides a current level Exec with the
ability to run essentially all applications software from the 1108 days,
i.e. user mode instructions?
If the latter, then PS/2200 is certainly sufficient and is available for
free (with registration) from Unisys. It includes a full current
release, including Exec, compilers, utilities, etc. (note, no source code)
If you want an Exec from back in the day that 1108 hardware was
supported, so your program could emulate the Exec instructions and boot
the Exec, I expect the odds are pretty slim. Exec went proprietary with
IIRC level 33, about the mid 1970s, so to be legal, you want a level
before that. In addition, Exec dropped support for the 1108 hardware
effective, again IIRC, level 36 (1980s?).
Also, note that you would probably need the source, unless you plan to
support the exact peripheral configuration of some boot tape you find.
And then you need the Asembler, MAP, SSG, etc. to be able to do a sysgen.
All in all,I would rate your chances of finding the source for a
pre-level 33 Exec, and all the supporting software as almost nil.