What an awesome channel. I really think two of your house rules are very clever. I figured most game time was spent with dice rolls and counting hexes for movement (to get the best Target Modifier).
Group Fire is a very good idea. 1d6 Pilot die, #d6 representing each weapon, roll at once. For location, re-roll using the weapon die's that hit with the pilot die. That's pretty dang quick without changing the game. Bravo. :clap:
Cluster weapons, I'm not really sure about how I feel about it, but it is still something to consider if the effect is pretty close to that of the actual chart. It's one of the more well-argued and thought out solutions I have seen, without resorting to the "box of doom." EDIT: This method seems to work well for weapons that account for per-missile or bullet hits, like SRM's and LB-X. LRM's doing full damage per cluster seems like it's a bit much. I almost feel like you can track LRM's by rolling 1d6 per missile on LRM5, 1d6 per 2 missiles on LRM10, 1d6 per 3 missiles on LRM-15, 1d6 per 4 missiles on LRM-20. So you're rolling 5 dice for each weapon. Then, after the clusters are figured out, apply it in 5 point damage clusters. I think this damage is more on par with the averages on the cluster hit table, but I could be very wrong. So roll to hit for an LRM-20. Roll cluster (5d6, result 1,1,4,5,3, so 3 clusters hit at 12 damage, roll 3 locations). I figure you can keep the black die, but have the minimal damage cluster as a translucent die or some other color.
Good luck getting the old guys here to change their minds, though.