If handwriting recognition is essential to you, you might be stuck with an LCD screen. Even if you used an alternative device to create notes, you'd probably still have to import to a computer and convert the handwriting with something like One Note. Of course, that would probably also require some clean up and corrections, so how much time away from the screen you'd be saving is unknown.
You will have seen me say this a few times now, but I love my Entourage Edge for curriculum stuff. Except for the fact that I can only annotate whole pages set at 100% view level (unlike a tablet PC where you can zoom in, write, then zoom out again), the Edge is my choice for creating worksheets with handwritten components. I was without any computer for about 4 months last year, and the edge was the only machine I had. It was my only machine, and I could do just about everything on it between what the LCD tablet side offered and what the e-ink reader/journal/note taking side offered. I'm really disappointed it's now a discontinued machine as I think it's great for educators. I'm lucky I bought one when the company and device was full of hope and promise, because it's not as easy a decision to make when you know it's been end of life'd.
I somewhat hesitate to recommend the Asus Eee Note to someone complaining of eye strain, as I could see some people finding it difficult to read from. It's just not as sharp/high contrast as e-ink, and sometimes looks a little washed out to me if you're not in really good light. It's not so much strain from the LCD as it is strain from feeling like you don't have enough light. I'm not sure whether one is any better than the other.
I've always said I think the Eee Note is perfect if you just want it to hold all your notes/sketches/ideas and don't often have to (or don't mind the steps involved in) getting that info OUT of the device and integrated with other technology. So, if you used it to get all your thoughts out, scribble out the test questions, and then (just as if you had done so in a paper notebook), went to the computer just to type in and format into your word processor.
But honestly, I think some people would be better served simply by writing on paper and scanning it in to the computer, then using pdf software to make adjustments. Or, many would be well-served using one of those pens that captures information that can then be transcribed/edited. (I don't happen to be one of those people, as I'm not looking to just capture my words, but actually care about the visual appearance of my handwritten words.)
And, from one teacher to another, don't necessarily write off handwritten tests and assignments! I routinely gave handwritten pages, and my students said they liked it because it seemed "friendlier."
If that's the case, you could totally scribble something up on the Eee Note, upload the note to Google Docs (then you don't get the background/grey border effect) which will be a .zip file that extracts as gifs, and just print those out as pdfs. Even then, you might be able to find an OCR software option to convert the text.
And, as has been mentioned in another thread, the Onyx Boox M90 and Pocketbook 902/903 are options to consider as well. I haven't had a chance to play with either of those, and I have found the Asus Eee Note to be a reasonable compromise for the much smaller price... and of course, I have an Entourage Edge so I pretty much already have the best machine out there right now.