From there, you can essentially blitz to Jackdaw's Dungeon quest. Most quests are just go there, talk, go here, talk etc. The only actual time sinks are completing the Dark Arts assignment, dodge attacks 10 times and 5 Infernus spells. You can bang out the 5 infernus on the mission by south Hogwarts where you complete the Merlin trial, then I found going north of Hogsmeade after the hide n seek game, there is 3 mongrels that you can do 10 dodges easy.