So if I am reading the code English properly, what I am asking is not
allowed even if the 110v (Class 1) wires are enclosed in Romex cabling
unless there is some additional "barrier" between the power and alarm
wires.
Right?

This is not allowed. SQLit had the answer some time back... Romex does
not belong in ANY conduit to begin with...

It is not required to be in conduit unless protecting it from physical
damage, I would 'suppose' it would exceed the fill requirements of the
conduit you are proposing to use, and it should not be mixed with low
voltage or alarm signaling wiring because of the insulation rating
differences.

Many alarm panels use semiconductor inputs, which sense either a opening
or closing of a circuit. Placing the wiring within close proximity to
other wiring can cause interference, and the alarm may either trip for
no reason or fail to trip when it's needed.

There is no need to place your romex in conduit. If you must use
conduit, use a separate one and THHN wire. You can also use flexible BX
cable with the appropriate fittings.

Jake