Learn English – “I was away last week” versus “I was out of town last week”

These don't mean the same thing.

"Barely managed" means "he struggled and succeeded by the barest margins". It usually implies the problem was with his capacity to do the work itself. "Had a hard time" has a more general meaning, like "he had some problems while doing something". It doesn't suggest anything about how well he did, nor what the problems were.

For instance, a single parent with financial troubles and no support from their family would likely "have a hard time" completing a degree, and might take ten years to do so, yet still get very high marks and never doubt that it would get done. This is not someone who "barely managed".

Neither one is usable in your example.

• The construction "opposite to" only works as an adjective: "The shop is opposite to the bookstore" works because it modifies the noun "shop"*
• "Contrary to" really works the same way. I could say "My beliefs are contrary to yours," and that works because it's modifying the noun "beliefs." But to say "I think contrary to" is to try to make an adjective work as an adverb.
• You could say "I think contrarily to you"—that's a perfectly valid adverb—but honestly, it sounds a bit silly. (Plus, "contrarily" has a connotation of obstinate, perverse, or ornery, and I'm not sure you want to suggest that you think in that way!)
• The suggestion of "I think differently than you" really is the best "fixed phrase" you'll get to fit this context.

* Ok, ok, really it's a prepositional complement, but let's keep it simple.