First thing is to go buy regular tire lube. It is much more slick than dish soap and water or even straight soap.
I then always start at the top of the rim. I put the valve straight down while mounting. Then start the top of the inside bead on the rim. I then reach up on the inside and clamp a pair of vice grips on the rim. This will help hold the tire on the rim while you start to work the bead on. The advantage of starting at the top is that the weight of the tire is helping you mount the tire. You just work the tire on a little at a time. You do need good tire tools not a crow bar and leaf spring like you can do on smaller tires. I have Ken-tool long tire irons just for tractor tires. Also make sure you have the top of the bead back into the drop center far enough. If it is not then you will never get the bead on without damaging the tire/bead.
After you get the inside bead on then install the tube if you are using one. Again put the valve stem down. I start the top of the tube over the rim and work my way down. I put the stem in the rim after I have the tube on the rim all around. Then put a little air in the tube so it stands up a little. This will help you keep from pinching it under the bead.
Then start the top of the outside bead on the rim. I still use a pair of Vice grips to help hold the tire from sliding off. Clamp the rim with the handle sticking straight up. Then work your way around the tire. Make sure you have the top in the drop center WITHOUT the tube being under the bead.
On the one you are having trouble with. You do have the rim on with the short side of the drop center to the outside??? On some rims the drop center is not in the middle. You can only mount the tire from the short side not the longer side.
Also on a larger tire like a 20.8 x 38 I use the jack to raise and lower the tractor to help get the tire into the correct position.
I would take the tire back off and start over. You are doing some thing wrong for it to be so hard in getting on the rim. Email me and I will send you my ph# number.