Always good to find a fellow Accord owner and CarPC beginner. I am also in the planning stages of my first carpc for my 06 Accord SE with manual 5-speed. In answer to your question, as far as I know the only way to get the unswitched (always on) power to where you need it is to run a new wire through the firewall. Everything I've found so far says that the unswitched power currently available inside the cabin won't be able to handle everything you're going to throw at it. Its best to add a new wire with a new fuse on it. I still haven't found my way through the firewall yet so I can't help you too much there.
I have a question for you too. You mentioned using a metra lower dash kit to install the screen in the lower part of the dash. This is right were I was planning to do it as well, except that I've only been able to find metra kits for single din stereos. Which kit are you planning on using? Any links would be helpful. Also, If you're installing the screen in the lower part would you be willing to sell the factory box that was there? I don't need the door, just the actual box that the door mounts to. If not that's totally cool, the dealer wants $160 for one and I thought this forum might be a better place to look.
Good luck with the rest of the install!