Trying to identify gray crumbly filler material

If it was my house I would not worry about it if it was intact (but I would not disturb it either), significant friable spread by convection alone seems unlikely. If I had kids... better safe than sorry, hire an asbestos abatement firm to test and remove/replace if necessary.

OSHA PEL (Personal Exposure Limit, max exposure over 8 hours on a time weighted average) is 0.1 fiber per cubic centimeter, max exposure over any 30 min. period is 1 fiber/cm³.

The "joint compound" is some form of mastic, which may contain asbestos if it was manufactured prior to 1984. If it does it's a very low risk because the fibers won't become airborne unless you so something reckless like sanding or sawing it.

The "popcorn" is vermiculite, a mineral which expands and forms small voids when heated. A low-density rock that traps lots of air has obvious appeal as fire-proof insulation. Unfortunately, tons of the stuff was mined and processed from an asbestos containing deposit in Montana. Short of having a qualified geologist look at it under magnification there's no way to tell. It's a bit more nefarious than the mastic because shoveling it up will cause fibers to be airborne. Wetting it will greatly reduce the number.

Keep in mind that a professional asbestos remediation involves a decontamination shower and negative air pressure to prevent fibers travelling to other parts of the building, either on clothing or air currents. They should also be checking the air quality afterwards to make sure fibers are wafting around.