I have worked up a simplified round and am also in the process of creating a second-by-second system. I wouldn't call the second-by-second more complex, but it looks that way on paper. Not done with it however, so here's the simplified version...
Step 1.) Roll initiative using 1d10+Average of Stats Bonuses.
The bonus to an initiative roll for physical actions (including movement) is calculated by taking the average of the characters Quickness, Agility and Intuition stat bonuses
The bonus to an initiative roll for mental actions are the average of Reasoning, Memory and Self Discipline.
Step 2.) Movement.
The combatant with the worst initiative is called upon to take their movement action first, however combatants with a higher initiative can choose to react to the movement of those with a lower initiative.
This is in order to simulate the advantage a combatant would have in winning the initiative. They are able to either move first to block a passage for example, or react to others movement and adjust theirs accordingly.
So, characters with the worst, or lowest, initiative will take their movement first unless someone chooses to react to that movement. They can move as little or as much as they want, but obviously no further than the character can move in a given round.
Most characters can move roughly ten feet per second at a full run. This translates to one, five foot, hex 5% action used. Obviously a character must have enough action left to perform whatever actions they intend to after movement (potentially with the appropriate penalty due to minimum action percentage needed to perform that action).
Step 3.) Declarations.
Players now declare their characters actions. Basically, anything other than movement, which has already occurred, needs to be declared at this point. The only exception to this are Instantaneous actions. For example, all of the following would be declared at this point: Attack Actions, Moving Maneuvers, Shield allocation, and Parry / Attack OB allocation
Step 4.) Action Resolution.
Actions are resolved in the order of the character with the best, highest, initiative to the worst, lowest, initiative. Characters can chose to delay their action and continue it later in reaction to another, slower characters, action.
For example, a character may wish to interrupt another character while in the process of taking their action (as opposed to merely trying to stop it in the first place).
If making mental actions (spell casting for example) you can use your In/Me stats averaged for an initiative modifier at this point with original init roll.