First off, to the OP: I like your black tractor better than your orange one - cool rig!
That said, Kubota really needs to put a 4x4 "on" indicator lamp on the dashboard somewhere. That is a cheap way for people to both be safer and reduce wear when they don't need it.
As for braking in 2WD: you can have all the ballast in the world but on a steep enough slope you will still slide. Weight always transfers to the downhill side of a vehicle on a slope. This means even with a heavily rear loaded vehicle a lot of that weight transfers to the front. A good rule of thumb is never go down a hill you can't back up. The reason is that if there isn't enough traction to back up the hill, there isn't enough to stop coming down, either.
4x4 greatly increases the ability of a machine to back up a slope and likewise stop coming down. But it is still possible to slide down a slope even in 4x4.
I flail mow steep reservoir dams as part of my job, and have a lot of experience on slopes in general with a tractor. The key is to use caution and never get complacent. I back up a 100-foot dam in two-foot tall grass probably a hundred times to mow down it. It's nerve-wracking every time, and I've had all four wheels slip momentarily while attempting to climb. The back end tends to feel very light during this process, despite 1000 lbs of flail mower hanging off the back and loaded rear tires. I tend to keep my loader on with the bucket attached for several reasons: a training wheel to prevent the rear wheels from ever coming off the ground, an emergency stopping method, and more metal between me and whatever I hit if I slide uncontrollably.
One last thought: if you can't stop and are sliding downhill, the best policy is to keep the tractor wheels turning forward under power, probably as fast as possible without having to change gears or ranges. This will help you maintain steering control.
Earlier this spring I was mowing a landfill in a 4/1 slope area. I mow sidehill on the 3/1 sections and when the slope increases to 4/1 I turn sharply downhill to avoid tipping. In this case, I forgot I was still in 2WD and went for a wild ride on my L4310. I slid for 100 feet and was just able to gain control before cresting the next tier of the landfill cap and likely crashing in a very severe manner. I am extremely cautious about 4x4 usage but became complacent or distracted in that moment. Let's face it, something like that could cost a life...extreme care is needed on slopes.