The top link will set the angle or plane of the attachment/implement with that of the tractor but has nothing to do with how far the lower lift arms rotate, ergo, how high it can actually lift something. Changing the plane of the attachment is handy for things like box blades and even your snow-blower. It's more intended to be a levelling device that also helps lift the back end of the implement more to enhance 'departure angle' which keeps the implement from hitting the ground when you're going through low spots. The relative motion of the top link and lower lift arms determine the geometry of the travel of the implement. Some implements such as brush cutters or rear mounted mowers actually have collapsible frames where the top link attaches to allow the back end to be pushed up as well as the implement to level itself on rough terrain. It will only allow the implement to drop down on the back end so much before the linkage draws tight and lifts the whole implement.
Move the lift links (between the upper and lower lift arms) to the hole closest to the tractor on the lower lift arms. You will lose some lift capacity, but gain motion on the arms, meaning they'll go lower and higher at the stops. I had the same problem with my LX2610SU, also exacerbated by oversize tires. My box blade wouldn't touch the floor when parked in my shed unless I extended the top link to the point the front blade didn't touch, meaning it wouldn't cut the soil going forward. Moving the bottom ends of the lift links allows me to lower it a full 10 inches lower than the surface the rear tires are sitting on. My chipper (800 lbs) is probably the heaviest thing I pick up, and I have no problem lifting that.