Mr. Chad -- I basically agree with AxleHub. Let me add a couple of opinions. (My machines similar to yours are Kubota, not Massey but the principles are the same.)
1) Fluid in the tires is almost always rear only and is for traction, not helping on steeper ground. Wheels spacers or anything you can do to get a wider tread in back is a huge improvement in avoiding tipping over or getting close enough to tipping that it becomes an issue. Fluid in the tires may help a small amount but very small, I say negligible.
2) On one
B2150 tractor I use 6" spacers of the Bora brand and find them to be excellent in quality and in the company having all the little subtle things figured out for compatibility and fit. With an added foot of tire spacing my
B2150 is daylight/dark safer to use with a small bush hog on steeper ground -- actually feasible versus NOT feasible ! However, I cannot use my midmountmower at all with the spacers -- tires will not clear the deck.
3) I'm using very large turf tires and it looks from the picts that you are using ag tires or maybe industrial tread. You probably will have more space than I do because of tire type if everything else was equal. Your worst-case will be with the deck raised. As was suggested, run a 1" board or any handy straight object across the back of your rear tires , between the rear tires and the deck wheels. With that board in place, does it clear everything or are the mower wheels too far forward to even get the board in there ? If the board clears, even while you run the mower deck up to the highest point, you'll be OK running the rear tires out as far as you like. In other words if the mower wheels are too far forward, then at some point you'd have a conflict trying to widen the rear tractor tires. I think you can see that but obvious things are often hard to describe in English.
Again -- if you want to be/feel more stable on steep slopes then move the rear wheels out as far as you can. As Axle Hub said, you don't want tires and deck wheels colliding AT ALL but on the other hand you really don't need a whole lot of spacing either.