But without putting it into the conditional with zou Would it be better to keep the sentence in its active form?
Can I say, (and forgive me, I just started learning the language so I am bound to make may grammatical mistakes);
"Zij hebben het verboden gemoeten"
That's a good try, and you're correct as far as your choice of which verbs to use goes, at least. The sentence you're looking for is "Ze hadden het moeten verbieden". But that's fairly complicated, because it's one of those cases where Dutch uses an infinitive ("moeten") where one would indeed expect a past participle ("gemoeten"). Definitely not beginner stuff, but then, your whole question is definitely not beginner stuff.
The "zij" or "ze" makes little difference, but as a rule you should use "ze" except when it requires particular emphasis; it's the same way with "je" and "jij", and "we" and "wij".
And "verbieden" simply because that is the correct infinitive. "Verboden" is the past participle, and of course also the adjective.