Since there's a lot more that goes on in my life besides songwriting, I have to squeeze in time for it. So, usually, I need some sort of assignment or project with a deadline to get going.

My First reaction was, Ehhh more often than not both actually. Maybee a full chorus melody and lyrics or a line or two. Often born out of non deliberate writing times, you know not scheduled.
Working and praising, then something of God falls on to your tongue then into your heart, you need to stop and write it down.
Never the same way twice in a row. I think song writing is as individual as we all are. Sure there are set rules about structure and content, is it descriptive, is it proclamative, or worshipfull.
In the end I feel if we are bound by any set pattern in any aspect of life/worship life, then we run the risk of becoming religious in attitude, a sort of 'that's how it has to', be mind set. I'm sure all the kingsway guys and girls who write all have different ways as well. It's the diversity of God that makes us all individual in expressing our one Hearts cry with our voice in worship.
Nice question, gets the thought process in action.

Blessings to all in Christ,

Steven Barr.