I have a pretty fail safe method for cooking BBQ baby back pork ribs at home.
make a rub and apply to ribs
wrap in aluminum foil
one hour at 325 in the oven
the reduce to 225 and cook for two more hours
Add BBQ sauce at the end and maybe back in the oven for ten more minutes.
Usually this yields excellent "fall off the bone" ribs. Last night however I did the exact same thing and the ribs were certainly not fall of the bone and a knife was needed. Too bad really because the rub was amazing. These ribs were more meaty than normal.
Is this a situation where the ribs need to actually cook longer? Further, could I put the leftovers back in the oven a day later and cook them longer to try and achieve the proper tenderness?
Your ribs were undercooked. Time is a guideline in barbecue, not an absolute. The folksy rule of thumb is "the meat will tell you when it's ready." Rather than watching a clock and taking the ribs out when a certain amount of time has elapsed, you should pick a time when you will start checking your ribs to see if they are done, and keep cooking them until finished. These are your cues:
Sight test - the meat on the ribs should pull back from the end of the bones considerably, usually around a half inch.
Bend test - if you pick up one end of your rack of ribs with a pair of tongs, the rack should be able to bend easily.
Probe test - you should be able to slide a skewer through the meat between the bones with VERY little resistance, if any.
Tear test - the meat between the bones should tear easily with just your fingers.
As far as reheating, it is possible. I would suggest wrapping them in foil, and perhaps putting some liquid in the bottom of the foil pack. It will not be as good as if you had cooked them in one stint, but it should still work.
Alton provides both a good rub and braising liquid, but I prefer to use beer rather than wine in the liquid and have tried it with other recipes that follow the same 'basic formula'. Mt. Dew or Dr. Pepper are both good choices.
It's almost certainly the "extra meaty" part that got you: just like a larger turkey needs more time to roast, these ribs could've used more time in the oven.
Baking the leftovers some more is not likely to get you good results. The fall-off-the-bone part comes with long cooking at an appropriate temperature; when you let the ribs cool, all that broken-down-collagen will firm up again, but not into what it started as. It'll have lost a lot of moisture, for example. Baking it again will likely just dry it out.
Perhaps some sort of wet cooking method could help, but then you'll lose flavor to the cooking liquid.