I had considered initiative modifiers as well, with the chits in a cup idea, but at a fleet level. I was thinking something based on the Aux systems - flag bridge, C&C etc. The fleets flag ship (or maybe the whole fleet) has it's C&C compared with the enemies. For every 100 points difference the side with the higher value can place that many extra chits in the cup, of either color.
So I have 8 ships, he has 6 ships. So there are 8 of my chits, and 6 of his.
I have a flag ship with 300 C&C, where as he only has 200. I can therefore place 1 extra chit in the cup, either his or mine. I'd probably place his during movement, so he is more likely to have to move first, and mine during Combat so I am more likely to fire first.