I appreciate the math but I use a color analyzer. My Jobo 5000 works well for this. I put one of the channels in "integrated" mode so that a diffuser is placed over the lens and over the light sensor. I place the light sensor in the middle of the print, place a diffuser under the enlarging lens, and click "measure." This will give me a log density value. Then I re-compose the print at the desired magnification and repeat the process. This time the log density value is different so I gradually open the lens diaphragm until the density values are the same. That way I keep the same exposure time and all of the doge/burn sequences are the same also. However, the larger print often needs a hair more contrast because of flare, etc. Therefore I do one test print of an important area of the larger print from which I can tweak the contrast before exposing the final, larger print.
Might sound complicated but it works well. If I have a detailed printing sequence dialed into my RH Designs Stopclock timer for an 8x10 print and then decide to do a 16x20, I can figure out the new aperture easily and retain the same exposure sequence. I suppose you could do the same thing with any enlarging meter.