I'm sorely tempted to ditch RMC and go with RMU, but I heard the current playtest files are in desperate need of being updated.
Do you have a link to an alternate rule set dealing with combat phases/sequences that I can port over to RMC?
The beta rules are a bit out of date, but the basic concept is still there, so I think it is still helpful to start with the latest beta rules. Also, perhaps JDale can give an update/summary/preview?
The most important change IMHO is the option of 'Faster Rounds', so I am hoping that JDale can give us a preview of that text box from the more recent beta files. Perhaps an updated list of AP costs would help too (or has already been released on the forums?).
In any case, the simplest system of 'faster rounds' is what we've called colloquially the 'Simple Round'. Instead of there being multiple Action Phases, characters just take turns taking all their actions for the round, one character after another. Each character has 4 Action Points and one Instantaneous Action to spend each turn. (This is similar to the Pathfinder 2e 'three action and a reaction' system, and not that much different from the DnD 5e system either). Every action has a specific cost. Characters just pay the cost and take all their actions when it is their turn. There are no phases for different types of actions in the Simple Round (or I guess you could say there is just one single phase for all actions), and there are no declarations. You just spend your points and take your action(s) when it is your turn.
RMU makes this possible because it treats all actions according to the same rules -- spells don't always go first, for example, and melee is not resolved differently than spells (in the RM2 phased system, for example, spells were resolved first and simultaneously but melee was resolved afterwards and sequentially; but in RMU, all the actions follow the same rules).
In practice (and I've used this new system for multiple groups for a decade now), I have found players pick this system up extremely quickly, especially if they have ever played DnD or Pathfinder.
If you want to simplify movement as well, you can do away with the pace chart entirely, and just have players pay Action Points for movement as well (this is an optional rule in the core RMU books).
So, for the absolute fastest and simplest system: give each character 4 Action Points and an Instantaneous Action to spend each turn; have them consult the Action Points cost chart to allow them to buy/take their actions each turn; and have them take their actions one after another, using the 'faster turns' and pay Action Points for movement optional rules.
I have my own houseruled list of Action Point costs that I would be happy to email you if you PM me about it, but you might want to go with the RAW first so that you can maintain compatibility.