If....and only IF, the teeth of the pinion gear are actually "jumping teeth" on the sector gear due to worn parts.............will you be able to correct for the shortcomings of this design.

As designed, turns to the left cause reactions in the steering sector gear that draw the sector gear into tighter mesh at the point of contact with the pinion gear on the bottom of the steering shaft.
Turns to the right cause reactions that push the sector gear away from the point of contact with the pinion gear. As a result, turns to the right increase the tendency for the mating teeth to "jump", while turns to the left decrease the tendency for the teeth to jump.
The construction of the sector gear is such that when the steer axle wheels are at "neutral" (wheels straight ahead) there are actually fewer teeth (and thus less travel or swing) on the "right turn" portion of the sector gear than on the "left turn" portion of the sector gear.
This uneven number was probably to limit the sector gear from turning far enough to permit the teeth from jumping even when the parts are "brand new" (which would certainly cause warranty headaches for the OEM).
Most machines that have this style of steering (meaning "single drag link") will eventually reach a point where wear in bushings and gear teeth will result in teeth jumping when turned to the left or right, depending on the specific layout of the steering components and links.
Not surprisingly, steering system designs featuring 2 draglinks instead of just one, are not afflicted with this unequal turn radius, nor the tendency for teeth to jump due to reaction forces.
Having 2 draglinks instead of 1 permits the reactions to cancel each other, no matter which way you are wanting to turn.

So, if you are hearing and feeling the teeth jump when you make a hard right, you can restore some of the lost motion by replacing the pinion and sector gears and the bushings/bearings that support their respective parts.

If you are not hearing/feeling/experiencing the jumping of teeth, you have simply become aware of the design limitations of this specific machine's steering system.

Hope this helps. I have a GT5000 and wondered about this when I first got it but found that it is the design of the unit. You can turn tighter to the left to mow around things like trees. Turns to the right are wider but that's where the discharge deflector hangs off and bagger if you use one so that usually isn't a problem.

"Hope this helps. I have a GT5000 and wondered about this when I first got it but found that it is the design of the unit. You can turn tighter to the left to mow around things like trees. Turns to the right are wider but that's where the discharge deflector hangs off and bagger if you use one so that usually isn't a problem."

That is the reason given by AYP, but I thought the GT was a Garden Tractor. It must have caused a problem, as they have quit making them that way. Thanks Guys Nuff said, Jim