There are a couple of devices here, but most of them run into one constraint you have or another:
https://kadavy.net/distraction-free-writing-devices/
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Physical typewriter: I think that electronic devices have put the era of correction fluid behind us.
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Alphasmart word processor: Lacks prestige.
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BYOK: Just a Kickstarter project.
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Freewrite: Whole line of similar devices. Some of these wonlt meet price constraints. Some might work. There's a $350 Freewrite Alpha.
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Pomera: Doesn't meet price constraints new. A used one might work; I see these on eBay for $100. Japanese-market-oriented, but E-ink and can clearly do English.
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Boox: As you mention, doesn't meet price constraints. Maybe maybe do a used one. I see someone selling a used Palma on eBay for $72, and this guy used his as a writing platform.
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Solarwriter: Mobile software designed to link an e-reader, keyboard, and iOS or Android device into an outdoor writing system. Could work!
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Remarkable: Won't meet price constraints new, but there are used ones on eBay going for around $200-$250 without keyboard.
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Kobowriter: open-source project to link a Kobo e-reader to a keyboard. The Kobo cannot power a keyboard, so some sort of external power source for USB is required. This specifically aims to be a cheaper alternative to the Pomera and Freewrite. Sounds like it requires some tweaking for different keyboard layouts and devices. I would not do this unless one is comfortable with this from a technical standpoint.
The problem with using "good" as a criteria is that nobody decides "what we need is a bad balance". People are going to have different takes on where they want that slider to be.