How much speed can a stock steering system take?

Been daydreaming for a while about building a 30 mph LT. Probably not going to happen any time soon because I have no money and less space (plenty of imagination though   ) but my noggin is smoking thinking about this. Basically what I’m wondering is if a chassis in relatively decent shape (new wheel bearings, under 2” play at the steering wheel, stock height, stock ball joints, etc) at what speed does stock become sketchy, and is play or COG the bigger issue usually? Thanks for reading and hope y’all are doing good. 

i did 39 with my craftsman lt1000 when it was stock width and lifted about 2" front and back. its sketchy but definitely doable. the biggest factor is how good you are at driving with the terrible steering on these things. you've gotta be moving the wheel constantly to correct yourself and you have to move the wheel a lot when there is play in the steering. id say 30 is definitely doable and a good speed. My craftsman was always able to cruise around there with no problems.

The issue is the geometry. They’re very twitchy with stock steering

Yeah, the big issue is in the front axle, rather than the steering box itself. That's where the jumpiness comes from. Lawn mower axles don't have enough geometry to self center, so they tend to dart back and forth, and slop in the box exacerbates that.

I've been working on that myself.  My Craftsman is Canadian, so its model number doesn't match anything in the US, but it's roughly the equivalent of an LT.

I did a pulley swap, to 5 1/2" front & 3" rear, which gives me around 30 mph.  The steering was terrifying - darting back and forth about 2 feet while racing down the driveway.

I started by rebuilding the silly plastic steering knuckle that aligns everything at the bottom of the steering shaft.  The hole the shaft goes through wears into an oval, allowing a ton of steering play.  I made a full-length steel bushing to line that hole, which got rid of a lot of slop.

Second, I replaced the tie rod with a homemade one, using heim joints at the ends.  Not only did that remove a bunch of slop, but it also allowed me to dial in some toe-in, which adds self-centering & stability.

Next. I removed the front axle (surprisingly simple & quick job) and found the plastic pivot bushing at the front was worn out completely.  As parts are VERY hard to get here, I made a new bushing out of aluminum & greased the heck out of it.  We'll see how that lasts....

Next on the agenda is to look at my drag link (from the steering box to the front end).  I know the front end joint is worn out, and I expect the steering box end is, as well.  I'll probably see if I can replace the ends with cheap heim joints....

At this point, the steering is still sketchy, but the darting-back-and-forth is limited to inches instead of feet.

I would strongly recommend a foot throttle to go with it all, as taking one hand off the wheel to adjust the speed is chancy at best when zooming along at 30 mph.

I can post pics of this stuff if you need 'em for reference purposes...