I can so relate to what you said: This idea of putting everything in head into GTD is exhausting and off-putting, and I don't do it this way. When I first got introduced to GTD, this is how it was presented...(put everything you have in your head into GTD) and it didn't work well.
But this is where "Deep Work" really helped and made the GTD operational for me. Rather than treating everything that comes to head as equally important, it's only the subset of things that are important that needs to be done in your "Deep Work" hours...Everything else is "Shallow Tasks"...Get your GTD working for the Deep tasks associated with your select few important projects and have everything else in your shallow tasks and experience the difference then :)
To answer your last question, I focus this method on my work life mostly (if you notice my screenshot of "Daily Page", you will notice that I only have hours from 9 am to 6 pm...) and the I only have daily pages for week days, and not for the weekend...Good luck :)