Just my thoughts on it.
1. The slow hive, depends on how strong it is. Is there enough eggs/brood to last through a queen rearing, mating, laying and brood maturing time span to stay alive?
The first option of course is to leave it alone and hope for the best.
The second is to put the new queen in there and see which one they prefer (leaving the cell".
The third is to let them finish and cap it. Then cut it out, introduce a new queen and use the cut out cell for requeening your existing hive or making the split.
Yes, try to keep the attendant's with the queen, they don't normally live very long anyway.