Here the minor works better not because of any balanced-unbalanced principle but because the major has an unexpected bad break. However, that's only at the seven level that the minor works better. You'd do well to be in the major if you're in little slam (unless your declarer play isn't very good).
Opening lead was a diamond just about always, ruffed by declarer. The insurance I was referring to above was to cash a top spade and ruff a spade in dummy before drawing trump. The odds are slim that you'll be overruffed, and indeed, if so, it would more than likely come from the long trump holding, paving the way for you to ruff another diamond return, draw trump and run clubs. The ruff of a spade in dummy would be a ruff in the short holding and would not block the suit or give you entry problems and would be just a little bit of insurance that might spare you from being dependent on the run of clubs, which won't work on a bad trump break. You can't knock out the fourth trump before attacking clubs since you'll have no more trump than your adversary and a diamond lead would now kill you. And if you can't knock out that trump before running clubs, a defender will be very happy to ruff the third round of clubs, denying you any use of the long clubs
The little slam should make with ease if declarer will only do that. "But wait a minute!" the impatient reader cries. "Do you really need the insurance. You take two rounds of trump, get the news of the bad break, and now cash a spade and ruff one, certain that if overruffed, it'll come from the long trump holding." That's true enough. So perhaps the notion of insurance isn't so important here as of flexibility. Those who went to the ace of hearts and came back to the king getting the news of the bad break will then have to cash a spade and ruff the second round, which I must admit would be a tad safer than ruffing a spade before drawing trump. For now a surprise ruff would necessarily come from the long trump holding, where indeed the defense has a natural trick. Declarer now re-enters the closed hand with a club.
Those who continued into the third round of trump were evidently not flexible enough to say, hey, wait a minute! I don't wanna continue drawing trump.
Four declarers went down in six hearts here, all going down two tricks, and one in grand went down two, also. It's easy to see why those in 6 went down 2 (and nobody was down one) because if you don't ruff a round of spades, your clubs are killed on the third round, another diamond lead wipes out your last trump, and now when you lose the fourth round of spades, the defense will cash a diamond trick. What was curious was why those in the grand made eleven tricks. It turned out that this East player didn't ruff the third round of clubs, but the fourth, allowing declarer to sluff a spade and save one undertrick.
You've got to be ready to adjust to any new information. Take two rounds of trump, note the split, cash the ace of spades, ruff a spade, get back with a club, draw another round of trump, and now just run your side suit winners until East ruffs in for the defense's only trick.