It is most likely the queen that is laying the multiple eggs, she wants to keep laying, but there are not enough bees to cover/take care of the eggs she lays.
Could be a virgin in there... regards using a test comb you only need to put in a small amount of tiny larvae and eggs, even cut a small section out, but if using a frame you can put it back in the hive you borrowed it from after a few days.
Sounds like you made the right decision for yourself if you were spending ages struggling/faffing about with the float and couldn't manage using the feeders without splatting bees.
I wouldn't use them either if I suffered with the same problems you do.