Well, I’m going to make another pitch for an I-Pad.
You suggested a limit of $400. For $329 you can get a refurbished I-Pad with 128 Gig memory. That leaves you $70 which can be used to get a I-Pad cover with a typewriter keyboard. Also the I-Pad is charged via a 12-volt USB port which meets another one of your requirements. Looks like it meets all of your requirements to me.
Also - and this is probably the best as far as I’m concerned - if you have an I-Pad, then you would have access to the Apple App Store. From that you can get access to a LOT of apps - both gaming and productive. A lot of the apps are free and those that aren’t are generally for less than $50. I have budgeting tools, spread sheets, presentation tools, stock portfolio monitoring, email, video, Boondocking, Tax Preparation, my library, my music sheet portfolio, etc. loaded on mine. Also in the past I was editing videos on my I-Pad, so have done some high-end processing on the I-Pad. The only apps that I actually bought was for the video editor (Luma) and Tax Preparation (H&R Block).
During my working years I was a software engineer at a major corporation and had all kinds of laptops and desktops. In my home lab I had two high-end desktops hosting 8 virtual systems all networked together so I could develop my multi-node software. To this I also had two laptops - the company one and my personal one. When I retired, I retained my laptop and my I-Pad. I got rid of all of the other equipment. Since I wanted to be on the road a lot, I chose to switch as much as I could to the I-Pad because I wanted to save both space and minimize my power usage. I’ve been amazed at just how much I could do on the I-Pad, how long the battery lasts, and how little power it consumed while being recharged. I now do everything on the I-Pad and I would still consider myself to be a ‘power user’.
I’m doubtful that I would ever go back. I’m constantly amazed at how much I can do, how easy it is to get work done, how simple the user interface is to use, and how easy it is to find free or inexpensive software apps for any need that I might come up with.