You can do HP+HK as a shortcut for Battle Butt.
LK+LP+MK gets you Pummel Horse.
What happens when you're doing this is the game sees 4,6 LK+MK. MK takes priority over LK, so you get a MK Tumble Run. The game them immediately notices you are holding LK (the MK input has already been 'used') which gives you Run-Stop.
Likewise, when you press MK+HK, the game gives you a HK tumble run (HK has priority over MK) and then notices you're still holding MK so you get Kanchou.
In the same way, you'll see that MP+MK gives you Kanchou, LP+LK will give you Run Stop and HP+HK will give you Battle Butt because it regesters the kick input first, gives you the run and then sees that the second input is being held down and gives you the appropriate follow up.