I find it really hard to get into CT1 on DPS (tried MNK and BRD), 60+ min queues I give up on or a pop for some other duty first.
I find it much faster to get into CT1 on Tank (my PLD queues aren't too long).
This is for solo queuing, haven't tried in party.

It would probably help you if you had 1-2 tanks in your party.
What does your "group" consist of? Do you have a full party of 8?