I would like to make a suggestion that addresses the fears of both camps. On one side you have the people for cross-server LFD. These people want faster ques and cross server would speed this up. People can disagree all they want, but it will speed it up in non peak playing times. On the other side people are upset that they might group with people that are not even on their server and thus cannot join their guild or group with them again. Here is my suggestion that fixes both of them.

First Step. (May not seem related at first, but it is)
All server transfers are free and you can transfer to any server any time you want. Even the extremely populated ones. Why is this a good idea? Simple. Transfering is free. Anyone who doesn't want to put up with a long que can leave. There are hundreds of people who never think to transfer servers and would if they knew they could. To make this easier add a button that suggests transferring to a less crowded server to the que message.

Second Step.
Allow for cross-server LFD.

Third Step.
Add a clearly visible icon next to people on your own server. People on another server will have a different icon. Anyone who clicks on this icon will get the server name from which that person comes from. Now people can leave their server (FREE) and join a guild/group on another server if they wish to party with them more often.

Fourth Step.
Add a ticker that shows wait times per class on your server. Do not make this function cross server. Just show the wait times for your server. This will balance out your server over time as some people love to dungeon crawl with any class. They will reroll what is needed.

Fifth Step.
Add incentives to any underplayed class on your server. If a tank is needed give them reasons to join the LFD. Add a random blue item drop that is equal to the highest level of the dungeon upon completion of a dungeon run. Make it BOP so they can only use it, sell it to vendor, salvage it, or whatever no selling to players. This lets them gear up faster and that is plenty incentive for most people to try out under played classes. People would even make alts to just play the class that gets the incentive at dungeon completion.

Just my thoughts, but I think this would increase community rather than deminish it as now all servers are your community. Some are just more local than others.