Out of interest, was your intended answer "where you started, facing east"?

FWIW, Claude Opus 4.5 gets this right for me, assuming that is the intended answer. On request, it also gave me a Mathematica program which (after I fixed some trivial exceptions due to errors in units) informs me that using the ITRF00 datum the actual answer is 0.0177593 degrees north and 0.168379 west of where you started (about 11.7 miles away from the starting point) and your rotation is 89.98 degrees rather than 90.

(ChatGPT 5.1 Thinking, for me, get the wrong answer because it correctly gets near the South Pole and then follows a line of latitude 200 times round the South Pole for the second leg, which strikes me as a flatly incorrect interpretation of the words "move forward along the surface of the earth". Was that the "usual error they all used to make"?)