Aaaand......................randzg HITS THE JACKPOT! (minus the part about gravity, because in this case gravity is negligible, however, your first statements were correct)

The holy grail (and counterintuitive) part of your response was...
"shuttle will turn 180 and fire rockets"...this is called the RETROGRADE BURN...doing this will make the shuttle's orbit smaller in radius (hence it will go faster as explained by moz_k2 et al, and by Kepler's laws), but then, once it nears the ISS, the shuttle has to turn around and face the ISS again, and fire its rockets, this is called the PROGRADE burn, to increase the size of the orbit, thereby slowing it down to slowly creep up towards the ISS.
Congrats randzg. I'll include a diagram/drawing of your explanation para mas masabtan sa uban. It's quite counterintuitive no? hehehe
-RODION