I disagree. https://dictionary.cambridge.org/grammar/british-grammar/adj...

With this the type (?) (universal) comes before the the purpose (co-ordination)

Despite the URL I don't believe this adjective order rule is limited to British English.

I suppose it depends on what is modifying what. If it's actually "universal time" and you have coordinated it, then CUT makes sense. If it's just "time" that you've both made universal and coordinated, then UCT makes sense.