I've got a timer circuit that's been working well (attached) that I'd like to know if there's a simple, inexpensive way to attach a sensor to either side of the 1 meg pot to determine it's value, introduce a scalar, and output the projected ON time, in seconds, of the 555 to a set of 7 segment LED displays.

 

The variable to track is the charge on the 100 uF capacitor.

If you don't need great accuracy, though, place an indicator knob on the 1 meg potentiometer shaft and mark the end points of its travel. Determine the ON time at either extreme of rotation. Mark the halfway point and see if that ON time is linearly halfway between the extremes. After that, you can add indexing marks to provide a reasonably accurate rough set to the potentiometer position.

 

Yup, but I was hoping to not have to desolder that 3mm surface mount pot and put a knob that is approximately the size of the rest of the circuit, that's why the 7 segment display idea.

 

That is a pain. The problem with monitoring the pot setting electronically is that it's going to introduce some current that will throw off the timing. Not to mention adding circuitry.