Ok, interesting. I ran ground fill and popped it into the SeeedStudio gerber viewer (this is where I’ll order my boards). Those ground points are gone (great!), but what I’m seeing now is the traces to my ground vias now seem to be just ‘absorbed’ into the ground plane, whereas what I expected was the for just the ground via to be connected to the ground plane, with traces appearing normally just like the rest of the circuit. And it looks like the pins that I’m trying to ground on the components themselves have sort of become their own ground seeds. Here are two images to illustrate what I’m talking about (the red one is from the Seeed gerber viewer). Is this expected/OK?
