Either way sounds ok, although would often signals the conditional. What about just using it is? Be careful. What if believe was in the past, believed? We believed it to be the best way out of this situation last year. Not We believed it would be the best way out of this situation last year. Or Instead We believed it would have been the best way out of this situation last year. Or We believed it was the best way out of this situation last year.

It's right to say (in my opinion)! The construction of this sentence is: I (S) believe (V) - skip putting "that" - it (S2) would (V2)... You just expressed using "a subordinate clause". It's right to say:)

Yes, it is correct. It sounds more natural to native speakers.