Electrical – Install ceiling fan on exposed conduit

Jay, I think you can use NM for this application as long as you do not cross beam. Cross beam refers to bridging between collar ties or floor joists across the bottom of said members, as opposed to drilling mid member and lacing the cable through the holes or following parameter beams and extending inward for each fixture along sides of 2X4's

My first choice would be BX or greenfield plastic coated flex raceway. EMT would be great, but maybe a little impracticable for your application.

If you can get enough access to install a BX connector on that armored cable, and if you can establish that the armor is actually a good protective ground (some armored cable only "floats" electrically), then you may be able to use a "remod box" to connect to the BX and claim your ground from the box. If none of those is true, then you really should do whatever it takes - cut access holes to be covered by the tracklight and install 2x4 remod boxes, whatever - to at the very least finish up that run with NM-B (Romex-type) cable. Given that this is for an overhead tracklight and you may not have any true grounds anywhere on that whole floor, and this house was probably wired long before grounding light fixtures became standard, you're probably legally covered.

I'm not as worried about spark containment as I could be, since the tracklight has its own termination box. Chafing of the wire insulation, though, is a bit worrisome; that's the largest reason for NM-B becoming standard. At the very very least, it'd be good to strip (without splitting) the outer sheath from a length of new NM-B and pull your two individual wires through it.