Edit: a year later and I find my own post about the thing I'm looking up. Good job past me.
My obsession is your benefit. From the stupid amount of time I spent last night looking this shit up, here's what I've reasoned out.
The Chuwi Mi10 Air is the bare minimum. It will probably work, but it won't be the best experience and it's leaving too small of room for error. The display isn't that good, the build quality isn't that good, no dual band wifi, bare minimum chipset, the keyboard costs 2/3 of the device (170 for tablet alone, 240 for the combo, though it's 10 bucks cheaper to buy them separately.) should the shadow service ever have some down time, you be stuck with a shitty tablet. Though I had a Venue 8 with the same chipset 2gb ram and 64gb in storage and managed to play civ 5 and css on it.
There is a higher level version called the Chuwi Surbook that has a N3450 chipset, slightly bigger build, 2 USB 3.0 ports and a type c for quick charging. Same ram and ROM, but has dual band wifi and b/g/n/a so that's a plus. That's like 340 though, but comes with the keyboard. This would be the best bet, but at 340, you're looking at refurbished SP3 prices, which would be a 100% upgrade over this.
But if you want to keep it 250-300 and hate MS:
Then there's this alldocube Knote with a 1080p display, N3450 chipset and type c. That's about $300
For 260 you can ditch the 2 in 1 for a regular laptop and get a 13" 1080p screen, Apollo Lake N3450, 4gb 64gb but with an M.2 slot. With the Jumper Ezbook t3 pro.
Then there's the Jumper Ezbook X1 that's basically a 11.6 inch t3 pro, but has a 360 degree hinge. That's 310.
I'd like to hear from people that have actually used them, but I'm 90% confident the ones using the gemini lake and Apollo lake with dual band wifi would work fine. For me, I found a good deal on a monitor (60 bucks for a 24" 1080p 75Hz with 1ms response time) so I'm going with my original plan of getting a mini pc and mounting that to the back for now.
I still want a 2 in 1 experience, but from what I've seen and for longevity's sake, I'm going to spend a bit more. On a better product that I know will work and not have something crap out in a year or 2 because I wanted to be a cheapskate.