Hey jumpthefence!!
i,ve had my TD for about 4 months now n yeah its inverted on me a hand full of times.....
but just like any kite it takes time to learn how to relaunch them...
i,ve got my inverted relaunch time down to about 1.5 mins max.... generaly when mine inverts i grab a handfull of front line n let the bar out.... (when u first do this it might take a few goes) but the kite will end up leading edge/underside down, then you have to pull one of the back lines to spin the kite around untill it catches some air, pull the bar in n whamo, fly it back to the edge of the wind window.
be carefull to not hot launch the kite (directly downwind) cause it will drag ur arse somewhat, no matter how much depower you have.
The best way to avoid an invert is to keep the back lines tight when ur eating it, or to pull ur stopper ball down far enough so the kite doesnt depower too much.
the more time you spend flying the TD it will just come naturaly, its a wicked kite with heaps of power/Depower
Enjoy