Most-efficient inexpensive way to speed/slow video track to sync with audio track?
Well you could download a trial 30 day copy of the legacy version of Adobe After Effects CS6. It allows a full unrestricted 30 day install trial. 

From there, you could take your footage in, place the master clip in a composition, and instead of cutting it, use the the time warp feature, which will give you smooth keyframes where you can adjust up the speed to X, then place a keyframe if you notice it begin to slip, and set a keyframe to slow it down a bit. This will provide ramping, which basically "cuts" the clip in half over and over again, and does all the math for you, to make the smooth changes in speed. Then render it out. Premiere might also have that function- it's also included in the CS6 Production Premium Bundle, google the download link, and you can install and try for 30 days without purchase.