There is some academic work in this area. If you're searching, use the terms "electrophoretic", "EPD", or "epaper" rather than "eink". Most focuses on either readability or subjective evaluation rather than eyestrain though. There's also a lot of related work on optimal contrast/luminance ratios independent of display type. Generally I think the reason people subjectively prefer eink is because the research tends to find that (for users that do not require visual accessibility accomodations) readability decreases after the luminance contrast ratio exceeds about 10 (e.g., Wang and Chen 2000), which puts eink in a natural sweet spot, and the need to increase LCD backlight brightness in well-lit rooms (e.g., Miyao et al. 2016).