Wow this thread got really long really fast. Just read the first two pages, so I don't know if someone suggested this or not yet but, here is the advice I would give:
I would suggest finding a party with the Party Finder tool instead of the Dungeon Finder tool.
Why?
1.) You can clearly state in the description that you are still learning your healing roll and would like to take it slow.

2.) You will only get people who are willing to assist you. If someone is taking time out of their day to help someone just go through a dungeon to learn their role, you can bet they are a nice person and could become a great friend in the future.

3.) You'll only be paired with people from your server. A good way to build a network and make friends.

4.) You'll likely get other people who are new at their jobs too, who want to learn as well. You can take it slow together.

Just two days ago I was waiting for a node to pop and was looking at the Party Finder. I saw a person who wanted to run Sastasha for the first time as a tank.
They were still missing a healer. I have a level 60 WHM and no other healer jobs right now, so there was really zero material benefit for me to enter the dungeon.
But I did just to help out. Figured it's a good way to build a wider network of friends.

Of course the tank was slow because he was new. But no one in the party cared because everyone who joined already knew it would be that way. Everyone was very supportive and helped the tank a lot.