My suspicion is that while the fleas road ship rats to the port cities, once ashore the fleas went to anything that would carry them. Livestock, pack animals humans, clothing, bedding and the like. Then as humans and stock moved at a rate beyond rats the fleas thus carried went from village to village with every traveler.
Flea and similar vermin were everywhere and while rats could be killed by ratters, fleas were just a part of life.
Some combination of what you suggest.
They die in 4 days without a blood meal. They also don’t reproduce well on just human blood. Needs to be other animals, preferably cats.
So hiding in blankets enroute is not going to work. They’ll die. But livestock, ya that will work to keep them alive, but breeding will slow.
It has always been a tricky problem since those guys showed the speed of plague spread exceeded rat travel speed.