Agree - when my tablet/convertible broke I stuck a small Linux distro on my eeePC701 and it let me Citrix into the office whenever I needed to show online presence from the airport lounge. The sweet spot is probably 8"-10" especially if the display is edge to edge without bezels. I did try an 8" Fire tablet with a Bluetooth keyboard case but that didn't work as smoothly.
As this is definitely an 'at need' device, I'd be curious about a Psion Revo style device (maybe larger but jacket pocket sized at most) with a USB-C connection to my actual phone which just serves as UI, relaying screen and keyboard and not doing any actual processing or storage. That would have a lot longer lifespan as it could move from phone to phone as I upgraded.