You may or may not be able to change the size of your tires. A Kubota L4600 was apparently available in both 2WD and MFWD versions.
A 2WD tractor is pretty straightforward to swap in different tires, all you need to do is make sure the tire has at least as much load capacity as what you are replacing, the rim fits on the hub, and that the mounted tires don't contact any part of the tractor. Rutting in turns also is due to the sidewall profile, the squarer the profile, the more it will rip up the ground in turns, and the rounder the profile, the less it will do so. So, if you put some implement/flotation or even used auto tires on the front axle, it will be a lot easier on the ground than rib implement tires. But, you will understeer (skid forward instead of turning) in sloppy/slick conditions as the lateral traction that causes rutting also lets you steer in those conditions.
MFWD tractors are much trickier, you will need to also maintain the ratio of rolling circumferences of the front and rear tires. You will need to either find a different front tire with about exactly the same rolling circumference as the ones you originally had, or you have to replace the rear tires with ones of a different size in order to keep that ratio the same. Otherwise, you will be pushing against the front axle with the rear axle (front tires are too small) or dragging the rear axle along with the front axle (front tires are too large.) That will either make one of the sets of tires slip and wear them out prematurely, or if they don't slip, your MFWD breaks.
You would want tires with a greater load capacity in order to have less sidewall squat. However, if the tires are rated appropriately for the front axle design load and you are making them squat a lot, you may be overloading the axle. If you have radials, they "cheek" a lot and will look like a bias ply tire that's almost flat even when properly inflated and not overloaded- that's just due to how they are constructed.
You would be better off in a subcompact with spacing your rows so that you straddle one row at a time rather than two as you would with a full-sized tractor. Thus, your row spacing would be equal to your tread centerline spacing, which appears to be about 35" according to Deere's published specifications. That would also give you plenty of space to fit your tires between the adjacent rows. Generally row spacings for tractor cultivation range between about 28" and 42" so 35" is right in the middle of that. The 17 1/2" spacing you would need to straddle two rows is very tight and you would indeed have trouble putting a 12" wide rear tire between those tightly-spaced rows.
Like I mentioned above, it would be difficult to change tire sizes on an MFWD tractor like the 1023E as you need to change the front tire size as well. No clue if proportionally larger tires on the front would even clear the tractor. If they did, you would also end up with the rear of the tractor sticking up in the air as you would be increasing the rear tire height by 4" for an 8" larger rear tire but only about half that much in the front. The front axle is usually the lowest part of the tractor and adding a couple inches of front axle clearance wouldn't really do very much for you. I do cultivate my garden with my tractor, and based on my experience you will want a foot and a half of clearance under the tractor. You would need to get either a smaller older ag tractor made in the days when cultivating was frequently done (such as a Farmall A) as they had high clearance for their size, or if you want a newer machine, you would be looking at a minimum at a full-sized utility tractor- but even then the MFWD front axles can sit lower than that until you get to even larger machines.
