So again, how much kinetic energy, and/or in terms of thrust (ISP
or kg/s in terms of fuel/energy consumption), would it take for a
satellite the size and mass of our moon, to be accelerated so as to
escape Earth by a rate of 38 mm/year?

Thanks so much for all the feedback. I'll try a little more input into
my three remaining brain cells and see if the amount of recession
energy can be realized.

The amount of energy needed to raise the moon's orbit by that 3.8cm/year is
easy.. Just plug into basic orbital mechanics, out pops an answer of some
1.25 * 10^20 joules per year, easier to visualise as a constant power input
of some 4 terawatt (4 * 10^12 watt)

The problem is that this is indeed the *resultant* of all forces
applicable. Just how big are the other forces working on the moon,like
frictional drag against the not-quite-empty vacuum of local space.(keep in
mind the moon orbits earth at about 1km/sec, and the earth whizzes around
the sun at about 30km/sec)?