1948 Allis Chambers Model B 1976 265 MF / 1983 JD 310B Backhoe / 1966 Ford 3000 Diesel / 1980 3600 Diesel
Sounds like you are on the right track to solve your issue. Very nice looking tractor by the way.
If you were to pull the FEL you will fine it would be awesome handling the box blade I expect but if you are using the box blade then the FEL may be handy at the same time.
Light duty after market FEL's seldom have a sub frame to the rear axles which often permits the design to move the weight of the FEL 12" or so towards the rear tires. Filled tires and rear wheel weights are two things most any tractor without a backhoe needs.
When you talk about getting suck in our clay you are talking about WATER but that is not your problem. We would call getting suck in sand getting 'hung' since there is no water involved. Wide as possible tires would be a plus in loose sand but not cost effective except at the time of purchase.
It will just take some practice and try to keep the nose pointing down as much as possible when working even if it means driving in loops to get to the high point.