Andalusia - trip sequence

It does. Depending on what time your flight arrives in Madrid (if you are early enough), you could consider heading to Cordoba after you arrive and save your Madrid nights for the end. That saves you one move, and could give you one night to add to any of your destinations. Like this:
Cordoba 3 nights
Granada 3 nights
Seville 4 nights
Madrid 4 nights
+1 night to be used wherever you choose. (I would probably use it for Granada or Seville.)

I agree with TTM about going straight to Cordoba. It's a short train ride,
there are plenty of nonstops, and I was going to say that you could
probably see Cordoba in 1 long day, so if you can get there midday,
get the lay of the land, and see the Mezquita the next day, you can spend
the morning the 3rd day finishing up and then head out.

Having 4-5 nights in Madrid at the end makes the last day more amenable
for a full day of touring, and gives you a better option to take a day trip in
that time to Toledo or Segovia.

For what it's worth, I was able to get an add on flight from Canada to Madrid on to Granada on my trip to Spain, for a minor amount to a Madrid return. My route was Granada 4 nights, Seville 4 nights, Cordoba 3 nights, Madrid 4 nights.

Thanks all!

I'd prefer to go straight to Cordoba because it's the easiest of the 4 to start a trip after a longhaul flight. It's the smallest and by far the most serene. I'd keep big bustling Madrid for last, especially if you're planning any day trips. Check the train schedules to/from Granada as well as the ALSA buses, which others have reported is a better option because there are few trains to Granada and times may be inconvenient, like the only fast trains may leave at 6.30 am and 1.30 pm.