If I would run this game (hope it's soon, but I'm DMing a D&D campaign right now), I would ignore how the round is divided in 2 phases, and just run it like I do in OD&D or AD&D, which basically is using B/X iniciative and round sequence (1d6 vs. 1d6, higher rolling group does all it's actions first, with a few common sense exceptions).
I am missing something that makes the 2 phase combat necessary to play this game?
If you want to simplify it and get right to the heart of the matter, just do it like this:
If the player announces an action he wants his character to take, and you feel it can be done in one round (10 seconds), but you also feel it will take longer than other actions being taken, just make him go at the end of the round (which is essentially phase 2).
That allows you to use the system you prefer, yet still retain the spirit of what AS&SH intends with the 2-phase combat system.
Player says, "I want to step 10 feet to the left and then cast magic missile." You reply, "OK, I'll allow it, but you are going at the end of the round."