You're asking what is needed to continue flight with a inoperative Standby Compass?
To be blunt..... if an aircraft is relying on the Stby Compass for operation, the crew has a lot more on their mind than just aircraft heading. We would be talking a complete electrical system failure (along with loosing the IRS battery feeding the #1 IRS). Chances of that happening..... slim to none.
But..... we're talking M.E.L. requirements here.
The 737-300 and above use three (laser-ringed) Inertial Reference Units. These are stand-alone units. They require no external inputs to function. All they need is to be told what the current position is upon power-up.
Older 737's (-200 and -100), the 727, DC-9, DC-8, and some MD-80's used a Flux Valve (magnetic sensing device near the wing tips) along with a mechanical spinning iron directional gyro. Every aircraft of those types only had two compass systems.
I have never seen an aircraft (nor will I) with both iron gyro's and IRU's.
Are you still flying -200's? If not, throw the gyro requirement out of that M.E.L.
As far as "positive control of ATC". I guess as long as ATC's used the old spinning ground radar, you could fly with traffic controllers monitoring your position..... but again, that's pretty far-fetched.
Pretty much the majority of flight environment data comes from the IRU's and Air Data Computers. A "minimum" of two each should be required for safe flight.
