Re: Will the queen move up?
Bees like to have the brood right below the honey, so if there is not too much honey in the top hive they will move up, with one BUT.
1 3/4 holes, the bees do not like having a hive divided by such a small hole. They will if need be, but only if forced. You may get lucky, but a surer plan would be rather than mess further with your bottom board, I'd suggest getting a piece of ply, or some kind of board, and cutting a hole in it equal to the internal size of the log hive. Nail it to the log hive, and put the lang hive on top. This will be a much more open connection and the bees and queen will feel fine about moving around the whole area.
Put three strips of wood under 3 sides of the super to be the same as the runners on the bottom board, so the bees will have a front door. Long as the queen is not blocked from laying by honey, she will move up.
Once she is up and laying in there, there will still be brood in the bottom and if the top hive fills with honey she may be forced down again. You are really wanting to get rid of the log as soon as possible so give the top hive plenty of room to store honey. You could also use an excluder to confine the queen in the top hive, wait 3 weeks then remove the log.
44 years, been commercial, outfits up to 4000 hives, now 120 hives and 200 nucs as a hobby, selling bees. T (mostly).