when you're in the tip stand try tipping the top wing back about 20 degrees.
Absolutely! This makes a huge difference. If you look at videos of Mark Reed doing tip stabs (stabs, not stands) you'll notice the top wing ends up a lot further away from the flyer than the bottom. This is much more stable than when the top wing is right above or even forward of the bottom wing.
So when you get your kite standing on one wingtip, try to emulate the finishing position of the tip stab. Also, once in this position the control is done using the lower line more than the upper line