I don't have much experience, but your goal is a lot like my own. It's all about the bees. The honey is just icing.
I would suggest that you could split your hive more than once this year if it is strong. Taking 3 or 4 frames (one honey, one brood, and one mixed with some pollen) with the queen and plenty of workers and starting a new hive might be doable multiple times in a year. Each time, the old hive would need to have egg frames ready to raise a new queen. If you find frames with queen cups premade (not uncommon) be sure to leave them in the queenless hive. If you found that successful here by the end of June, you might try it again in August. Since honey is not your goal, you won't mind being behind in your production. If it works right, you hit the winter with three hives. You could easily make that 6 the following year, even if you never catch a swarm.
Having multiple hives really helps in splitting. It would be much better to take a frame each from 5 hives for a new hive, than try to split one hive to make a new one. That's a trick I'm sure you could do more than once a year, which would really boost your numbers.