I think what you are saying is what I am running into with websites or YouTube videos about increasing ground speed on a cheap lawn tractor. Unless I find something or someone tells me differently, I'm afraid I'm going to be looking at putting a hitch on the car. That is NOT what I would consider ideal, but it's looking like the most reasonable option. I guess in the long run it might be for the best, At least if I have a hitch on the car and a trailer I can pick up equipment in neighboring communities. I have passed on 3 pretty decent deals on 42" and 46" lawn tractors recently. One in particular that I should have just jumped on. The owner wants it out of his garage and I'm about 99% certain it only needs the valve lash adjusted, He did like so many other owners when that problem pops up. He bought two new batteries for it and then bought and installed a new starter. Of course, it's still doing the same thing. I even offered to fix it for him, right there in his garage. He flat refused. He said he was sick of it and wanted it gone. His asking price was WAY below the value of the thing if it was serviced and running. I passed on all of them only because I have no way to haul them and I won't go asking friends to help if I'm going to refurbish the things and sell them. I'd have to pay for that help and that starts getting touchy when you mix $$$ and friendship.
Putting a hitch on an existing car can be problem as well
A friend is into Subaru's however putting a hitch on his current one would cost $ 3800 ( aus)
Apparently you have to change the computer, brake sensors , some of the rear lighting harness and you have to fit the Subaru specific sub loom for the trailer wiring , you can not just splice a trailer pug in or the computer will register a wiring fault & go into "limp home " mode ( so much for too much technology ).
The dealer also suggested replacing the rear suspension , another $ 2750
So all up $ 6,550 to fit an unbraked tow bar and an extra $ 180 for an electric braked trailer ( + $ 655 for higher capacity alternator )
A rough dented used F350 goes for about $ 4000 + $ 250 for a tow bar if not already fitted .
An L300 like I drive will go for $ 2,000 & most come with tow bar fitted
A Toyota High Ace is about the same price & a Lite Ace about $ 500 less.
Consider actually fitting out a van as a service van which is what I have done .
The L300 will take a 36" mower in the back or a any tractor if you slip the deck off
I keep a set of on site tools ( cheap ones ) in the van an empty 5 gal oil drum ,a sump pump ,a couple of jacks , 4 jack stands , a 6' length of rectangle steel tube ( to slide over blades ) plus a tool box of hand tools , some shop towel & hand cleaner.
As for parts, an assortment of fasteners ( that often break or fall off ) a 5 gal drum of SAE 30 & 10W 40 , 2 grease guns .
Before I go to do a service I slip in a set of blades & belts for the mower(s) I am going to look at .
I try to do a couple at a time to reduce travel time .
By doing this I do not end up getting my street vehicle dirty, seats greasy, body dented etc .
It also prevents the street vehicle ending up as a repository for broken parts