I might have missed something, but it sounds like you may have flooded your hive with excess sugar syrup and caused a mess from the top feeder onto undrawn foundation. Excess syrup or sugar water can't be handled and makes a sticky mess of the bees when they have no place to store it.
I'm old fashioned about this (some say) but I always believe a new package, in a new hive NEEDS an ENTRANCE FEEDER and short entrance reducer to give it some protective room to guard. Keeping up with a feeder jar can be daunting BUT you have a visual way to know when replenishing is required.
And day 14 on the second queen?? That's a scary, you lost THOUSANDS of brood (mostly eggs and larva mind you) and in-house workers NEED that building of comb and nursing task to complete their cycles of life in a normal and productive fashion. Marching around with a caged queen gives a hive very little incentive to product cell structure. I don't read when the first queen was released, and if she appeared healthy - curious if the bees were calm but productive or lazy and absent-minded? A bum queen (totally bum) isn't that common, but I think I would have saved her and tried a few hundred workers and her back in the shipping cage with a piece of foundation and syrup to see if she laid eggs then - could be she never mated?? I'm sure that happens from some videos I've seen and the great slide show TWT put on the forum.
Many will argue WHEN to get the queen out of the queen cage - I have always removed the plug, waited 4-5 days and check to see she is released. If not, I'll break through the candy seal, return the cage and check again the next day. I honestly have not had to manually pull the staple and open the cage more than once and she GLADLY walked out and among the workers.
If your comb was drawn out, a hive top feeder is a great thing, many people will tell you to use it all the time - I won't argue that point now. But your hive was in a perfect position for robbing if the queen wasn't out and about the hive and brood wasn't in the making. Best wishes with the next package, keep a close eye on it and YES an entrance reducer set to small is plenty of room for them to travel to and from with, you'll know it is time to expand the width as they bottle-neck up when returning from the field.