Like selcuk said, its more about the rise and fall times than the actual clock speed. There are a million great youtube videos on signal integrity that will do a better job explaining that than I will.
Thoughts:
1) You are probably fine with doing whatever for the board with the addressable LEDs. They are pretty forgiving. Not a guarantee, but it will probably work as is assuming your power and ground rails are sized to handle the current (assume about 0.05A per LED).
2) 4 Layer PCBs are cheap enough now that it doesn't make much sense to use 2 layer boards if you are at all concerned about ground/signal/power interactions. Worry about board costs when you get into the 1000s quantities.
For a quick personal project just get the 4layer.
www.JLCPCB.com3) I like the back-mounted LEDs with the board cutouts. That's a cool idea. I don't think I've seen that with those addressable LEDs before. Let us know how well they solder like that.