The best avatar.

The problem is that I draw incredibly slowly.

This isn't a problem, but rather a lack of practice. But it seems like you're working on it, judging by the comic. )

And when they produce amazing art and caption it with "speed painting, sketched in half an hour, didn't even try," I feel inadequate. And spending months perfecting a single picture is realistic in terms of ability, but not in terms of patience. I have a bunch of unfinished canvases lying around from a long time ago, and I doubt I'll ever finish them.

Speed paintings are made for the purpose of practicing. But you're probably aware of things like "100 faces in 100 days," "30 hands in a month," etc. I constantly see this in blogs of people who enjoy drawing.
No one perfects anything there – what comes out, comes out. Maybe tomorrow it will be better.