I actually find horses that are responsive way easier to work with and I am 100% sure that I would have no problem working with your horses whatsoever. What I find more complicated is horses that appear slow (or lazy as you call them) and then they are extremely reactive. I have never seen a quarterhorse act like that. I know a women here locally that works with warmbloods and she says that when someone sent her a quarterhorse she thought that she should pay them to work with the horse because it was soooo easy. I know some AQHAs can be a bigger challenge than others - of course - but in general and comparing to other breeds especially warmbloods these little AQHAs are a piece of cake. I can assure you that I have worked with lots of AQHAs.
It all comes down to how you handle them a lot of the time.