Maybe the DM42?
programmable? kinda
rugged? a steel or titanium case, not sure, but yes
keyboard? should be good based on prior form
clock? yes
alarm? don't think so
e-ink? yes
weeks of battery? yes
This device may be hackable in the future, but it will be released based on free42 and Intel's quad-precision decimal library which I think will make it the most accurate handheld calculator.
Another option might be the numworks calculator[2] which runs python and is open source. But doesn't meet your other criteria.
A third option might be the Gemini - a folding clamshell that runs linux.[3] or even the pocket chip? [4]
[1] https://www.swissmicros.com/dm42.php
[3]https://www.indiegogo.com/projects/gemini-pda-android-linux-...