Back to the original question:
How do you pastors do it?
Some do it well; some do it poorly. Sometimes there is a lot of pain, and (to be hones) sometimes it is with a sigh of relief. But mostly you just do it because that's part of what you signed up for when you signed on to itinerate.
I've heard that when clergy leaves a church, you aren't allowed to initiate contact with anyone in the old congregation for a year.
That may be an annual conference rule unique to Florida; I don't know. That particular way of saying to give the new pastor space is not how it has been worded to us in my conference.
Do you feel like you're abandoning friends, or is it really just a matter of moving on to a new job?
Where you've made friends it feels very much like this. It is one of the hardest things about being a pastor. I'm in a situation where I moved 5 hours only to have the mother-in-law of my wife's best friend from our previous congregation to be living directly across the street from us. How do you not say "Hi!" when they are sitting out in the front yard to watch the 4th of July parade?
Last month I was back at my old ski hill where I taught lessons for the last 5 years, visiting old friends completely unrelated to any church I've ever served (and in a complete different state even), when my last youth group shows up. And they all want to hang out with me.
Sometimes you can't walk away. On the last occassion, I just sought out the new pastor who had brought them, and sat down with him. Other times you wave, you make small talk, you may even engage in conversation about family, but you don't talk about the adminstration of the church and you don't evaluate (or even ask) about the condition of the ministry. The connections that remain are related to praying for the well-being of individual people. You're not concerned with policies, procedures, or programs of the congregation.
As you leave, since you are the chair of the board, I think that you may wish to make your decision to leave known at a board meeting (give the pastor a heads up you're going to make said announcement in advance of the meeting). Better for you to announce it, than for the pastor to have to report it. I don't think that "slipping out" really is all that helpful. There will be speculation either way. But if you don't address it yourself, you leave it for everyone else to fill in the blanks with their own ideas. You don't have to go into detail, but you can lay to rest any rumors that you have heard bandied about when other people left, because you can rest assured that they will all be suggested as reasons for your leaving.
And if the reason is the pastor, then I still suggest the above. You can avoid poisioning the well by just saying that you're needing a change and though you don't know where you're going to end up, you pray the people of the congregation can support you personally in your decision because it has been one of the hardest you've ever had to make.