"I make sure I make it at the start of the scheduled time on Saturday, I've seen the line long enough that not everyone makes it before Mass starts an hour and a half later."
Perhaps your priest should take some more time from his busy week to offer this sacrament.
If someone needs it, they can have access to the sacrament. He's very clear about that. We recipients also have to be responsible on the scheduling, we're the ones who know what we need. Arriving at the end of the scheduled time and expecting no line is, mmmm, hoping for the best.
It's not like most parishes are overflowing with priests twidddling their thumbs looking for something productive to do. They really are pretty busy.