I'd be curious to know where you read that the tree shouldn't be topped, and that doing so would kill it. I've never heard that, and my personal experience is that any fruit tree can be topped -- and topped repeatedly. I've never lost a tree due to topping, and I've had a lot of fruit trees over the decades (well over 100).
Think about it this way: in nature, when a tree gets too tall and sticks out above the
canopy, that tree will absorb a lot more of the energy around it. Positively, it will capture more of the sunlight. But negatively, it will also absorb more of the wind, and extreme wind will snap it off. So the trees in the forest work in concert with one another. They share the
solar energy via the
underground root network. In a forest, you'll find stumps of old trees that were cut down 30, 40, 50 years ago, and they still have an active root network that is kept alive by the other trees that surround it, feeding it sugars and other nutrients. Crazy, huh. So trees like to be a member of a team. Tall trees share with the shorter ones, particularly the baby trees in the "nursery" on the forest floor below. They collaborate far more than they compete. Thus, the tall trees gets pruned by nature (strong winds) and kept in a healthy ratio to the other trees around it.
I used to subscribe to the "single leader" theory of tree pruning and development. Mostly, I liked that look in my orchard. I wanted to utilize that vertical space, so I let the trees get tall and only kept a single tall central leader. And it lead to problems like you're facing -- overloaded and spindly bent trees. Now I aggressively cut them back to about 3 feet in year 2 or 3 to encourage strong lateral growth, and then I keep them no taller than 5 or 6 feet. Just last winter, I went through and cut all my plums and pluots to 5 feet, and this year's harvest has been amazing. Why no taller than 6 feet? Because that's how tall I am, and I can only reach about 7.5 feet comfortably. I don't want to drag a ladder all over the orchard, or have my arms ache when I'm pruning, thinning and picking.
If it were me:
1. I'd aggressively thin the fruit, starting at the top of the tree and moving downward. Take some weight out of that tree right now, but continue to let the tree grow and store energy as it prepares for winter.
2. Next winter, I'd take a sharp pair of loppers and give the tree a serious haircut. I'd cut the main trunk/leader off at about 4.5 feet or so. The sooner you do this (in the life of the tree), the smaller the wound will be and more likely it will heal-over.
3. Going forward, continue to take mass out of that tree every dormant season.
Honeycrisp are notorious for overbearing and then for the apples to become massive -- bigger than a softball. So for these first few seasons until your lateral branches become stronger, you may wish to aggressively thin the apples earlier in the season to keep the weight on the branches down.
Best of luck.