What makes you think this is a catastrophe? The bees were succeeding well enough to swarm. That's not a catastrophe. It would have been nice to head them off, of course.
>I've went throught the hives and seen my strongest hive (before 10 swarms that is) is now honey bound. I have researched and I am quite confused on how to correct this. Almost all brood frames are filled with uncapped honey. The new queen that I have seen has no space sans maybe one side of a frame to lay eggs.
Classic signs of swarm preparation.
>I have read that I should/could take some frames of uncapped honey and place them into a weaker hive and replace it with a frame with new foundation. Then the next bit of research I do says absolutely DO NOT use foundation and only replace with a aframe of drawn comb.
Either will work but you'll get the best effect with an empty frame and no foundation.
>How should I go about taking care of this before the remaining bees swarm yet again?
Open up the brood nest. Foundation, no foundation, drawn not drawn. Just open it up. My choice would be no foundation.
Put enough supers on to give the bees room. If they were drawn I'd say pile them on, but since they aren't I'd probably try to keep it to what they can fill with bees so they don't chew the foundation up.
Here's the long version of my form of swarm control:http://www.bushfarms.com/beesswarmcontrol.htm
You could also do a split.http://www.bushfarms.com/beessplits.htm