Another thought:
There may be something physically keeping it from remaining in float. It could be a stone, a stick, a mud-dauber nest, or the like. If you can access the actuating area of the joystick, it might be worth a look before doing something more drastic. (I'm not familiar with your model.)
Then clean the area thoroughly and then hose it down with WD-40, or similar. Then apply a bit of oil to the moving parts.
The maintenance of a FEL requires that the area be lubricated every so often, like when greasing the FEL. Since you just bought the tractor, there is no way of knowing what has been done.
If the tractor has been left outside or power washed, it is possible that water has gotten into the valve and something has rusted, causing problems. (See below.)
And BTW, it is not recommended to disassemble the valve. I did it once and never again. There are ball bearings and small parts galore that are very difficult to keep track of and tend to disappear and/or roll away.