If I understand TMIT's HA strategy correctly (especially with Kheshiks) a key is to get Flanking II and attack only with the first move, reserving the 2nd for a possible withdrawal; even against spears, 50% retreat probability helps a lot. I've never tried it, but plan to, One Of These Days.
I use a combination of flanking II guys and guys going down the combat line. If the defenders are strong, I lead with flanking, otherwise against flatland archers in cities for example I'll just attack them with combat II (> 70% odds of winning outright, and OK retreat odds).
One unit gets sentry. This unit lets me see cities from far enough away to know if I can take them out or if their garrison is too strong and that I should blitz the next city. Stick n move is very effective against the AI (and a lot of humans though you might want to raze cities in that case...very demoralizing and it's hard for them to chase your stack while they can't retake what was lost)...every time a city is taken, there is less productive potential. Not only that, but this tactic FORCES the AI to fight on flatlands or lose all but 1 city (which eventually gets over-run). However with sentry it's often difficult for the AI to strike my HA forces when I don't want it attacked.
The results are fairly ridiculous. Only deity AIs have turned it away...I've cut down pacal (who is actually easy despite UU), gilgamesh, shaka, and basically every other supposedly-difficult to rush civ on immortal using HA rush. Too easy to catch the AI out of position.
The trick to rushing multiple civs or an entire continent is to stop when you lose momentum with 1 civ, heal, and continue to the other ASAP. You can damage tech pace so badly that nobody gets feudalism even after 500 AD, which means eventually you can cover the whole continent.
If you do that, mind diplomacy, and wheeze to emancipation + cottages (or anything really, but cottages make it super easy), you win. Your conquests kill the world tech pace and that allows you time to catch up in tech as the largest empire.
Through all of this, it is important to note that EARLY MOMENTUM is CRITICAL. Don't attack garrisons that run the risk of stopping your attack entirely.