So, I did some brainstorming, and came up with a houserule that should accomplish the goals of the initiative rule, without having to call out each rank/suit combination individually.  First, my assumptions about the goals of the initiative rule (which are hopefully correct):
A) Neither player knows for certain who will activate next, except in very rare circumstances (such as having the highest suit ace).
B) In spite of not knowing for certain, both players can make educated guesses about who will activate next, based on the strength of their hand.
C) The player with a greater number of unactivated units has a higher chance of activating next.

With these goals in mind, I have come up with this process:

1) Both players are dealt a number of cards equal to the number of units they have, as normal.
2) Both players reveal the highest card currently in their hand.
3) The player with the higher card out of these two activates a unit.
4) The player with the lower card draws a new card off the top of the deck.
5) Repeat steps 2-4 until all of one player's units have been activated, then the other player finishes activating his remaining units.

What do you think?  As I said, it seems to accomplish all the goals of the original system, unless there are any goals I overlooked.  And it should move things along much quicker.