Since movement is calculated per Combat Turn, how far can a single character move per Action Phase? Can a character move up their entire run rate in a single Phase even if they roll a high enough Initiative for multiple passes?
Yes you can use your whole movement rate in your first Action Phase (there are no rules against it).
You can even do this with a Interrupt Action if a Grenade/Area Spell is thrown your way.
Run for your Life action, Run & Gun, p. 125
[...] a character can make an immediate Interrupt Action to flee. The character [...] can use any amount of available Movement to move away from the incoming attack.
Note that Initiative Passes do not necessarily stand for time intervals that partition the Combat Turn.
This model may not be perfect, but if you'd use rules that require the characters to split the movement between initiative passes, the results could be even weirder:
Opponents A and B both have the same running rate X and both are X meters away from a gun. Both want to get the gun first. Now A gets to act in only 1 Initiative Pass and B gets to act in 2 Initiative Passes.
According to the rules the following happens:
- B uses a Free Action to get to the gun and 2 Simple Actions to Pick it up and Shoot.
If B could move U meters in the first Initiative Pass and V meters in the second Initiative Phase the following would happen:
- B moves U meters, which is not enough to reach the gun. Now there are 2 options: Sprint and hope it's enough to reach the gun (depeting all actions in the Initiative Pass making it impossible to pick up the gun) or move only a part of the distance. We'll go with the latter for simplicity.
- A moves to the gun, picks it up and shoots.
- (Just to make it more absurd. A hits and the Initiative of B was 11, and 1 before the hit. The hit deals enough damage to reduce B's Initiative to 0 costing him the second phase and the rest of the movement.)