I write the same way both of you said you do now. I usually do some rereading before I start a new chapter or scene, at least reading the previous scene to make sure it flows. If I haven't worked on the story in awhile, I usually at least skim the last few chapters to get back into the flow of it. When I actually start writing, it takes me a long time because I play around with word choice and revise/edit as I go, so that by the time I'm done with the chapter, it's pretty much ready to go. Even then, I like to sit on it for a day so that I can proofread it with fresh eyes, and usually I catch a few typos or make a few changes in wording then.
When I first started writing fanfic, I'd crank out a short chapter in one sitting and post it right away, and I did that almost every day - it was rare for me to go more than a day or two without updating. Now it takes me a lot longer to finish a chapter, and my updates are more sporadic, but the quality and consistency of my writing is a lot better. I said this in another thread recently, but quality over quantity!