Is there a way to quantify smoke in meat while cooking?
Well... yes. There are analytic chemistry techniques used to measure the concentration of phenols, which are the primary contributors to a &quot;smoky&quot; flavor. You could test samples taken from the meat at different depths to measure penetration. You'd need a reasonably well-outfitted chemistry lab to do a good job of this.
Honestly, though, objective measurements are not the right way to go about this. There's a reason food scientists do both chemical and organoleptic tests. Objective chemical measurements are always going to be an imperfect approximation of subjective experience. If the color of the test strip tells you something's not very smoky, and your tongue tells you it is, which are you going to believe?
If what you're looking for is a way to reliably compare the results of multiple attempts over time, just take small samples and freeze them, then compare them [using your tongue] once you're back at max taste.