You could always just make a post on the forum designated to your server and ask for people interested in doing the dungeon to log on @ a certain time, a time most suitable for you, so that you'll have people to do the dungeon with... You already know how to use the forums, I can't imagine that you'll
need an auto-party system to get anywhere in this game.
Cross server auto-partying systems have been known to create chaos in other MMORPGs. I hope most of you are not ignoring the downsides and trying to hold the positives to outweigh them. For you to use one source of communication, claiming that you need a new source to find parties looks ridiculous.
http://forum.square-enix.com/ffxiv/forums/114-COMMUNITY
I suggest you start using these forums and finding people interested in playing the same time as you. I've seen multiple threads on these forums where people are joining together at certain times and planning ahead.
Certainly, you've heard of the phrase, "plan ahead"?
When dungeons come out I plan on hanging out around the NPC to find a party. When it reaches the point to where I'm unable to find a party to do them, I plan to use the forums to find a party of people who is also interested in running them with me. Not only does it help increase community awareness, but it allows a chance to prepare ahead of time, discussing tactics.
With those that have used a cross-world partying system that auto-parties for dungeons, most of us have heard of and experienced the negatives of the feature and would not like to bring Final Fantasy XIV down to that level. If it ends up being part of FFXIV, I don't plan on quitting, but I feel that the negatives will outweigh the positives.