Couple things to keep in mind.

Rice tires with those deep cleats will go through about anything and keep you moving. However it's possible that you are going to be putting a lot more strain on your final drives and other driveline components. You may also not have enough power through the variable speed pulley/belt set up to keep them turning in really sloppy conditions ?  Definitely need shields for the variable speed belts and pulleys to keep the mud off them.

Also modifying the rear axle to a wider stance for clearance and running larger tires will also likely add more strain to that rear axle which was known to be a weak point anyhow especially at wider width settings.  

I'm not trying to discourage you at all just wanted to make you aware that should you go that route you may be setting yourself up for  possible other problems down the road.

I've got Rice and Canes on my 6620 T II and they will absolutely go places you thought you could never get through including low spots with standing water. However the resulting ruts are a mess to straighten up later.  How are your springs for getting ground worked to fill in ruts filled with water ? They don't really float over the mud they just bite deep into it to keep you going. I'm very careful running things anyhow but I take a lot of extra care when I'm forced to run in those conditions to not tear things up. I was told they can be very hard on the hydro coupler. I checked it when I had the hydro out to fix a leak on the control shaft and it was fine.

I previously had a 4420  with variable speed and got into muddy conditions at wheat harvest a few times. Regular tires would just slick over and you could not go anymore. A trick others have done is to reverse the drive tires side to side they will stop you moving sooner but will not allow you to get in so deep you can't back out. With the reversed tread you should always have more bite to back out of the soft ground.

I know where your coming from with wet ground. We have quite a bit of tile but a very old and overloaded main that nobody wants to address which limits things and there are always a few places that are a challenge.

Good luck with whatever you decide. Might be able to find a later Uni Harvester with RWA for not much money that you could pick corn with. Might even be able to adapt your head to use on it if the Uni is narrow enough. I used to have a neighbor that ran a Uni picker with a 443 JD head on it.