Ok, this could be a ramble, but let's give it a try...
First, I'm not sure that being analytical is necessarily the problem in itself. However, if we become too critical of our ideas we stifle them before they can flower. That is a problem.
What we need is some way of not analysing or applying any critical thought to our ideas while we are in the idea phase. If you are analytical, you may like De Bono's "6 thinking hats" - in this case, I am talking about the green hat. (
http://www.mindtools.com/pages/article/newTED_07.htm).
If it works for you, you could construct songs in a very linear fashion. You could analyse them, create affinity diagrams.. really go to town
The trouble is, not many people can create like that.
What is involved in a song? At its simplest, I see 3 things that need to be created.
1. The idea
2. The music (can be split into numerous parts, but the basic melody and rythm)
3. The lyrics
If I try and do these sequentially, I can get stuck fast. If I approach it from an analytical angle, it can't all come to me simultaneously.
It may be tempting to start with The Idea. There is nothing wrong with that. However, once you have an idea, stop! Get another idea. Don't move straight into the music unless you already know how it sounds. Don't develop the lyrics unless you are drawn by their rythm.
So what constitutes an Idea? Well, it could be a feeling. It could be a single lyric (one line or phrase). It could be a theme. It has to be more than "hmm, something about insertsomeintellectualideahere". You have to have an emotion attached to it, I think. What does it feel like? How does it smell/look/sound .. most importantly sound. Can you associate a visual with it? What is the soundtrack? Can you weave a story around it?
If you have an idea and are drawn into writing, and are excited by it, go ahead. Often, however, I find that I am not ready. If that same thing happens to you, jot the idea down.. it can always be picked up later. Keep a list of ideas. And get another.
You can do the same with lyrics.
However, many of us find that the key to unlocking some of this stuff is the music.
I can't create music analytically (and that helps me), maybe some people can. I can develop it analytically, but I don't create the initial musical essence analytically.
I mess around, take risks and find something I like as a start point. I play it over and over and try and make it more interesting. I might get analytical at that point, trying different progressions, alternatives, changing rhythm and tempo.
At some point, however, I just go over it and over it.
Sometimes I find a lucky mistake that works. Sometimes words just come into my head. Often they are crap. That's fine, they are flowing.. let them come..
.. la da di da di da di da
.. la da di da di da di da
.. this prison is bursting at the seams
.. la da di da di da di da
.. Do you know what tomorrow brings
.. etc...
At some point you think.. "hmm, where did that come from?". Maybe a line .. I don't know .. "Where do we go from here, my love?".
Out of our subconscious comes something that we were censoring, something that strikes a chord. A relationship that is foundering? Whatever it may be, a new idea starts to form and there is a skeleton to build on. Then the graft starts.
If that doesn't work for you, try jotting down all of the random lines on separate pieces of paper. Arrange the pieces and form a pattern .. I bet there is a pattern (after all, it came from one person's mind and that person has human preoccupations that they are processing).
Then don't censor yourself. Develop it. If it wants to change into something else and that seems better, let it. The only objective is to establish a basic song - it doesn't have to be the song you started on (you can always do that one another time).
Once you have that basis, the rest is polishing - repetition, editing and hard graft.
And once you have one song, you are on a roll.
There is no secret except.. don't wait for inspiration. Inspiration is something that happens while you work imho. And find any method to disrupt overly linear thinking until you are settled on a complete idea (with all 3 parts) and have a clear vision of what you are creating. Until that point, use the stuff that you can't do intellectually while listening to your inner voice. In my case, that is the music.
...
hmm.. better stop.. I am starting to ramble.
I do wish you luck though. Just write something, anything. The next thing will be better. If not, that's fine too (we can get stuck all over again if we write something we really like, because we don't think we can top it). Then we are back to the same .. we need to just write something (anything). If you have something, you can build on it. If you have nothing, you have nothing to build on.
The first rule of song-writing? There are no rules.