Could you please give it a try? Thanks.
Who needs keys when you can pass through walls?
It could be optimized by doing the door skip faster but it's good enough for me. I took the liberty of starting a run at the beginning of the level with a few keys already obtained so as not to have to restart the game each time. Anyway, it makes no difference to the final time as I don't use the keys.
Here is the run in 2:33