a lot of but not all plugs are soft lead, and pulling them is the best way to realy clean the passages, otherwise, as you've noticed the passages aren't positioned to do a good cleaning.
for re-plugging them, I've melted small beads of a harder solder pressed them in and used a softer lower melt temp solder to seal it. though if you want you can use almost anything to plug them. I've got a dozen different types of solder so it's just more convenient for me.
Ken