The thing about the printing press is not the technology involved, which is pretty simple, it is the ideas involved. Once you have seen the process, it becomes obvious.
The press itself would have been imported, probably a bit more than once and then copied mercilessly.
I think that thorn's days were numbered already and y was simply used in print to save a couple of pennies.
Perhaps someone more invested in this would be able to look at the incidence of thorn in English handwritten text and printed text.
Another recent oddity is the letter r. My parents (so think born: early 1940s) were still writing r as a backwards and downwards curved squiggle, within a word. As a leading letter it would look like r or R.
For good measure, let's take a unique oddity: naïve - note the double dot over the i. It's a French word and let's face it, that thing is almost certainly a British affectation.
I own a copy of "Usage and abusage" and I probably ought to throw it into a fire 8)