I generally write a few quick details about the dream and then later type them up in more detail.

Recently, I've started a morning ritual of getting up, taking a picture of my paper DJ (which is then automatically uploaded to Google Photos), and then when I am ready to type up the whole dream I just load the picture on my computer and use it for reference. That solved my problem of having to take my physical DJ to my computer area, which used to be very annoying.

For RCing to prevent false awakenings, you could try autosuggestion -- maybe a mantra of "when I wake up, I will do a RC".