Yes you have to take care that geometry points are sequenced properly - and you can do that with xparticles.
Unfortunately I can´t open your scene and I´m afraid you can´t open mine. So I try to describe the necessary steps.
1) take care that your geo has points spaced at your convenience ( caps regular grid etc)
2) now emit from this object - shot one particle per point , stick to object . On emission tab choose an action for particle death -> spawning action, one particle only.
Generate spawning emitter and set particle speed to 0 here.
This spawning emitter gets a trail object -> connection mode straight sequence.
3) add a xplife modifier - kill particles mode and for falloff add a field that fits your needs for desired filling.
Now key the field positions according to the sequence you want to do your filling. In my scene I move a cubic falloff from bottom to top of the letters within some frames. Don´t do it too fast.
Play the animation till all particles changed emitter - means trail is completed . It is wise to give both emitters different particle colours so you get a visual feedback for progress. Do an present state to object on the trail and you get a spline.
Don´t try to fill this spline yet - will be fatal 🙂
This spline has to get a connect segments from spline menu and optimise first.
Now you have a spline with your desired filling sequence meeting all your geometry points and you can use this in a different system ( or just delete the generating system and set up a new one) to cover in object vertices ordered mode...