Thanks, I appreciate all the help and advice! I was travelling for the past week and only now had a chance to try fixing the printer problem again after a while.
I first tried Front Fine Art feeding the paper instead to see if that helps (although I’ve successfully printed to the same paper – to the best of my recollection with the same settings – using top feed option).
At first, I had difficulties feeding the paper using the Front Fine Art option as the paper didn’t seem to easily go into its place. It was as if something was preventing it from curling a little bit to reach all the way to the back. However, lifting the paper a little bit while pushing it in its place helped with this and the feeding finally worked this way, too. I googled the problem and noticed that this is a design property of the printer, or that at least many have had the same problem.
Yet, also with this alternative feeding mechanism the head strikes persisted. What’s worse, some smallish black flakes (like dry ink or something that I could blow off of the paper) could be found pretty much randomly around the print. Also, with the first try using front feed option, there were dark smudges about an inch of where the print area starts, after which the white head strike patterns started:

I also tried manually adjusting the paper thickness (the default setting with Premium Luster, suggested to be used with this paper by Canson, was 3 and I tweaked it to 4, whatever that means) but all that seemed to fix was the dark smudges. There still were head strikes all over the paper and black flakes as well. Also, in the very edges of the paper there were some tiny multi-color stains.
What was common to all the problems I noticed is that they don’t start until the printer has printed about an inch of the picture. Therefore, I thought that could it be that the whole problem has something to do with the mechanism that moves the paper forward as the printing progresses?
@Mark D Segal, I’m not sure what driver settings you mean and where I could see them. I’m happy to provide that information if you think it might help.