Mac video capture / recording at a resolution larger than, and aspect ratio different to, native display
Apparently, it may be possible to get the OS to output a higher resolution than the native one. It requires some config files tweaking. I can't vouch for this method.

If you just need to show, say, the middle third of the screen, then another possibility is to zoom in to provide a larger source for ffmpeg to upscale. Depending on the size of the area of interest, this might not make much difference. 

Of course, I dare say, 1680 --> 1920 should be an easy upscale post-recording with hardly much difference in perceptual quality unless your items of interest are very small.