I've had some time to think about some of the workings of ICRPG. Being a tinkerer at heart I can't help but want to come up with material for it.
I'm also a big fan of highest roll starting, then going clockwise after them as advocated in the book, it's already my favorite method in other games. But I know that method may not be everyone's cup of tea, having options never hurts. The one change I make to the core method is I like using a d10 instead of d20.
My first idea was giving a scene a target based on having the drop or advantages in combat. Surprise attacks and having the high ground could both be examples of having advantage. A straight stand off in the streets would be a 10 as neither side has advantage over the other. While a group of goblins jumping out in ambush could be an 18 for the players as the goblins have the upper hand. The idea is whether or not the round is stacked in the players favor to act first. If the players get the drop on some foes lower target to 8 or possibly 6. The idea here is every player rolls an attempt against the target number. Those that succeed go before the opponents do, those who fail the target number will go after. The order stays the same until the situation changes, as having the drop usually only lasts a round. Unless the players or ambushing goblins were just so effective in the first round, their momentum gave them advantage in the second also.
The second idea I had was keeping the clockwise from the initiative winner as core, but instead players anounce their intentions and would roll the corresponding effort die (with no modifiers) connected to the action they plan to take. If a player plans to cast a spell he would roll the spell effort die, if a warrior is attacking with her sword she would roll the combat effort die. If a player is doing some simple action that normally would not require an effort roll then they roll 1d4-1. In this method the lowest roll would go first. Then go to the next player going clockwise as normal. This method can be more complicated if that is something the party wants and instead each player acts in the order of their roll from low to highest.