Herman,
You have a classic hydrostatic transmission in that machine. One of the smoothest and most reliable ever designed and built. Honda designed their first one back in the 1960's, so they have been around. Look at all the better tractors and you will find the same tranny in those.
Let me caution you on heavy ply tires and larger sizes and diameters. Most ATVs come with a 2 ply tire and this is for a reason. These tires are like riding on a soft pillow compared to the heavier tires. They will crawl over obsticals and handle much better too, allowing easier steering and delivering more HP to the ground. That's the ultimate goal right there. When you go up in tire size you lose HP and torque, and you will notice a difference, especially if the machine is used for working and pulling. The only problem with 2 ply tires is they are prone to pinch type damage between wheel and large, very large rocks. Again, if that isn't your style of riding then you have nothing to worry about.
I have had a Honda Rubicon for years, rode it for recreation and also worked it, so my advice is from pure first hand experience. Actually, the machine was to big for working in tight woods, I use a little TRX300FWD for that.
Bigger tires will not bother the computer at all, but again you will lose performance. See, most people don't work, or ride these machines real hard, so losing some of the performance to larger tires is no big deal. If you do put larger tires on you must keep the same differential on front vs back. If you don't you will have drive problems because the differentials are designed for the specific tire diameter differential on front vs back.
Good luck,
.
Craig