Hi UTCenturion
I have no experience with liquid filled or solid tires myself, but I do use my BCS 740 for mowing, so perhaps you can use some of my experience nevertheless.
The "standard" tires might be the best choice for certain tasks (like tilling), but I do not think mowing is one of them

With the 5x10x20" wheels, I had 11 cm (just over 4") ground clearance when parking on a hard surface. Most of this clearance was gone as soon as I drove unto my lawn. You will probably mow on even rougher terrain, so I expect you to hang up a lot. For mowing, I think big diameter tires are the best choice. Without extensions, this means 6.5x12x23" on your tractor. The relative small 3" increase in outer diameter might sound modest, but instead of giving just the 1 1/2" extra ground clearance as one might expect, I almost doubled it to 20 cm (8")! As a bonus your tractor will run 15 % faster.
Stability comes from a low center of gravity (CG) and a large outside track width, so mounting your wheels in the widest possible setting within the width of your mower, will give you a good stability. Adding wheel weights will lower the CG, and thereby also increase stability - and traction, by the way.
I look forward to hear about your experience mowing "steep pastures and creek banks". Depending on the size/weight of your mower, I find it very difficult to mow across a slope steeper than 10 degrees, as gravity pulls the mower downhill. An older BCS Owners Manual recommends mowing across a slope when walking behind the tractor. I have tried that, but I simply was not able to, so I have to mow up and down.
Best regards
Jens