I don't have an answer on the bead but are you putting a little air in the tube first? Doing so makes getting it in cleanly a lot easier. And the really simple trick to getting the right amount of air - don't use a pump or inflator. Blow the tube up with your lungs. (Sadly, this only works with presta valves, not Schrader unless you can figure out how to depress the spring. It's such a useful trick that it is a reason to consider presta it you aren't already using it. You will need a sleeve to reduce the rim valve hole. Any bike shop.)

In any case, just enough air to inflate the tube, no more, will make the job easier with much less chance of pinching the tube as you work the bead over the rim. (Sometimes I have to let a little air out to get that last bit of bead. That's OK. It did its job.)