pure hardly runs at all, hard to start, arc jumps wildly all over the place.
as to the splitting, sure sounds like bad manufacture. what brand are you using, and have you tried switching? one size too small an electrode for the current shouldn't result in splitting after a few inches of weld. it would start balling up. oh, and 1/4 isn't the next size, 5/32 is then 3/16
Agreed, probably bad batch of tungsten. I've done every bad thing you can do to tungsten I think, and the only time I've ever had splitting issues was before I learned not to snap them in half.
My recommendation: When cutting tungsten down, hold it at a 45º to your grinder wheel and twirl it until all the way through. That gets you two pieces with a (roughly) 45º end on each, and just a little bit of grinding to get your finished tip.
A coworker ran 3/16" tungsten in an air cooled torch, many years ago.

That was on an Aerowave 700 maxed out. What a beast those were. Until they caught on fire...
Can anyone explain why pure tungsten is not recomended with Dynasty? I only have an old 300/300 transformer machine for AC tig, the Maxstar 200 gets used for most of DC tig. Never used a Dynasty...
A tip: You can use pointed Thoriated or Zirconiated (do your own research please, it's been a looong time for me) on Transformer machines in AC mode. The tip won't last very long, but it gives you so much better control than a big ol ball on a pure tungsten.