I found that I had the best success getting my thoughts down on the paper when I told myself not to look back and edit. So I decided to do an experiment and made a mini-webapp to do this.
In the app, you can only see the current line you are typing, and you are allowed three backspaces at a time (combinations are allowed).
There's also a visual of blurred text in the background to help you feel like you are achieving some progress.
This was just a fun experiment, but I wanted to get some feedback to see if people actually would want to use this sort of thing.