Sounds like you have some really tough ground to keep mowed! Advice so far is spot on... and just to keep things in perspective, consider this: it's actually better to beat up the mower rather than the tractor. If you get a heavier mower, it may just identify the next weakest link in your mowing system. If that is something in the drivetrain of the tractor, rather than the mower, your next repair bill will be a whole lot more costly than buying a new mower gearbox or re-attaching a wheel.
Just a suggestion about your 30 acres. You might see if anyone with a mid-size dozer would go over the property and grub any larger stumps and rocks for a reasonable price. Not a full re-grading, but just so you woudn't have it quite so rough when mowing. There are plenty of contractors looking for work these days. Maybe you could get 1-2 days work out of one for a reasonable price.
Just a suggestion about your 30 acres. You might see if anyone with a mid-size dozer would go over the property and grub any larger stumps and rocks for a reasonable price. Not a full re-grading, but just so you woudn't have it quite so rough when mowing. There are plenty of contractors looking for work these days. Maybe you could get 1-2 days work out of one for a reasonable price.