Are any ATLTs insured and/or registered?

In my state (NY) ATVs must be registered (all) and also insured if they are operated on property that does not belong to the ATV owner (I guess).
My agent has said "Unfortunately, we do not have a policy for the lawn tractor. There is an agency that may be able to write the policy. You can try the **** agency ***-***-****. Hopefully they can help. Thank you!"

NY law says this (trimmed a bit despite that it's still long):
An all-terrain vehicle (ATV) is any self-propelled vehicle with two or more wheels that is manufactured for sale to be used primarily off-highway or in off-road competitions, and that is no wider than 70 inches and weighs no more than 1,000 pounds. This does not include vehicles manufactured exclusively for travel on snow or ice which are subject to other laws and regulations.
ATV REGISTRATION
An ATV must be registered with the Department of Motor Vehicles (DMV) if it is operated anywhere in New York State, including on the owner's property.
You must have a valid NY State registration to ride your ATV in New York State, unless it is
• only used for agricultural purposes or not-for-hire snow removal on private property
• registered in another state to a resident of that state
• only used at special events (competitions)

INSURANCE
You may not operate any ATV anywhere in New York State, except on your own property, unless it is covered by liability insurance. Minimum required coverage is $50,000/$100,000 for death, $25,000/$50,000 for injury, and $10,000 for property damage in any one accident. You must show proof of this insurance upon the request of a judge, the police, or a person claiming to have suffered injury or property damage from your operation of the ATV.

There's nothing about lawn mowers as far as I know. I would expect them to have the agriculture exception but does it count for any configuration the chassis might be turned to?
If you guys know an agency or company that would provide the coverage specified I would appreciate learning of it.

I tried to get a quote from Progressive but they asked what year my vehicle is and I don't know.
The S/N does not appear to be a date code, at least not the simple code they expected.

I know @Maine Mud Mower has done his previous ATLT for the state of Maine. He may have some pointers. You can try him here or hit him up on his FB group. "Maine Mud Mowers" https://www.facebook.com/groups/MaineMudMowers/ look for "Neil Greenleaf"

I dunno what the laws are in Texas, but any officers would have to trespass on private land for 2 miles before they even get to my land. So I'm not very worried. Plus I've actually led a deputy around my land on my tractor before, LOL. Once we got there, he said, "Man I though this was going to be slow! I turned my radar on, you were pushing 16 mph!" hahaha

My area of concern is mostly the Right Of Way road adjacent to my property and in the future, I can foresee somebody straying over one of the back property lines where the terrain drops off suddenly.
If or when something happens I'd like to have a reputation as a law abiding citizen. I have a habit of landing in gray areas, though, and this is a fine example.
Probably just worry about nothing.

"unless it is
• only used for agricultural purposes or not-for-hire snow removal on private property"

Its a lawn mower, silly copper! would be my reply to any inquiry.

There are balers, mowers, all manner of ag equipment running up and down the roads everywhere I've ever been, just getting to the next field or whatever.  Just leave the mounts for the mower deck on your rig and ride happy.