OP, good for you for recognizing that you can get a little lazy too, as can we all(pass the chardonnay please :D!!). So many people don’t even get that far, and it’s great you really do want to be challenged 
Stick with it and be on top of things, and you may just end up enjoying those lazy rides. And absolutely the more horses the better (within reason of course, it sounds like you are not a dead beginner)
While I do enjoy an easy horse every now and again, one of my favorites rides was a horse that you had to have a what we called a “Come to Jesus Meeting” (see Redhorse post for an idea) at the very begining of every single ride. Two mintues of get up and go, I don’t care if your’re ticked off that you do in fact have to move forward, ended up with a super fun ride that aught me a lot. He wasn’t a school horse, he had done the A/O jumpers and some Big Eq before we got him (A/Os is probably what soured him a bit, getting burried to huge fences one too many times) so I could push him more then perhaps you’re trainer would want you too on the schoolie, but I ended up enjoying it because I could really ride him. It went from me dreading the exhausting ride, to me actually asking for him (first thing in the morning mind you before I was too tired). He took your seat, he liked support, he let you make adjustments up there, and once you got the go, he would do just about anything if you asked him properly. Even your lazy schoolie could surprise you when you figure her out!
Stick with it and will you may just feel much more acomplished getting that kind of reaction out of sleepsalot or one similar, then you will out of a naturally forward horse.
