Maybe try making them deeper? It’s going to be tough to get paint into the scores, if it were me I’d try going a bit deeper and then using something like rub n buff or thick body acrylic and force it down in there.
You need a wider cut (score) so they’re open enough for the paint to fill. You can do that by defocusing the operation. This will make the beam wider at the surface than a focused one will. To do that you need to tell it the material is thicker than it really is. That raises the height of the focal point which is usually set at the material surface.
The beam is like an X where it’s wider at the top and the bottom but tightly focused in the middle. That’s the narrowest the laser can get (IIRC it’s something like 0.007" but don’t hold me to that 
). That’s great for not making a big kerf but what you’re trying to do you want a bigger kerf.
Yeah, making them deeper/wider would be the first thing to try, and I also like the “force it in” idea.
…yet another approach, which may not work but which would be worth an experiment or two, would be to thin the acrylic down, then use needle-tip applicators to place the thinned paint directly in one of the slots, letting surface tension suck it away from the point of application, taking it further along the slots?
Please note, the above suggestion is purely based on my experience using hyper-fluid adhesives, where they will wick into any available crack (which is the point), and is not coming from personal experience with thinned acrylics. Just seems like a potentially adjacent mechanism.
Deeper and wider like the gang has already said. also do a search for the paint pens that people have recommended in the past. they work very well for that application. I am at work or I could open the dang drawer and just tell you what they are.
I’ve had decent luck in the past with golden high flow acrylic and a sign squeegee and a sand afterwards to remove what didn’t go in (when I did it on acrylic I kept the mask on so it could be worth a try of masking and doing the defocused beam to get a thicker score)
I totally agree. That keeps the paint in the lines as well.
