Major Sway Problems! Any ideas!?

Sounds like getting rid of the first set of tires was a good move, not all tires are equal. The real issue here is most likely a lack of tongue weight. While I don't recommend you drive 70-75 with a trailer, the trailer should still be stable at those speeds. The danger is if something unexpected happens at that speed with the trailer, slower is safer. Everybody needs to decide that for themselves but a 65 mph limit on trailer tires convinces many of us to keep it to 65 or nearly so.

Add some tongue weight and let us know how that works.