This sounds plausible.
I'll try that, just to see if it helps, but I don't think constantly switching between 2WD and 4WD is really a practical solution especially when transit times are in the order of 30 seconds. The time lost changing drive mode would almost certainly be greater than the time lost just going slower. The 5100 does not have a way to quickly/easily switch between 2WD and 4WD, unfortunately.
For the loping, it's always a problem with a load in the bucket. The basic way that always works is to reduce the energy input by slowing down. But if you want to go faster before the loping gets out of hand you have to reduce the energy being transferred between the tractor and the FEL. To do that, you add some damping either to the tractor motion or the bucket motion...or both.
Dealing with the tractor first, you reduce the bouncing energy from the tractor by slowing down, reducing tire pressure, and shifting to 2wd.
BTW, since the front tires run at a slightly higher ratio than the rears, there's a lot of torsional energy stored in the 4wd drive shafts when traveling with so much load in the bucket that the front tires can't slip.That takes the form of the drive shaft and transmission windup. So not only for anti-bouncing, but mainly to reduce wear on the whole drive system you DO NOT want to be in 4wd when traveling with a load in the bucket.
Considering the FEL side of the equation, if the pivot pins for loader arms and bucket are tight and unworn, you can reduce the bouncing energy by soaking it up in some sort of damping mechanism. These dampers are called "easy ride" or "comfort ride" systems and there are various types on the market. Some are options when you buy the FEL, and others are aftermarket. All of them work....some better than others. Long's simple & inexpensive aftermarket nitrogen cylinder damping were mentioned by Jeff back in post #11 or #12. They work. Other systems have more complex damping cylinders, cost more, and work better. Some models of Kubota FEL offer a "comfort ride" as an option; that's a factory version of the same thing. All the comfort ride options work by storing energy in roughly the same way in a pressurized accessory cylinder. If your household water is on a well, you have a bladder pressure tank that is stores pressure in a similar fashion.
So with some thought, you could make your own damper with a pressure tank, valve, and some hoses. The picture that Jeff posted on his message shows everything you need to know about how it works.
Most of us just expect the tractor to lope when traveling with a full bucket. The fact is that no matter what you do, they will all lope at some speed on just about any surface. If we have some sort of active ride control like comfort ride we can go 50% faster before it starts to lope, but lope it will.
So what we all do is to reduce front tire pressure, shift out of 4wd, slow down, engage ride control damping if we are lucky enough to have it, and keep the FEL loader pins lubed to reduce the wear.
And sit back to enjoy the ride.
rScotty