Expiry isn't the issue. In America (and Canada I'm pretty sure) you have the right to use a patent at a fair cost determined by a court. Or you can try to just use the patent anyway and wait for the court case to come to you.
Some exceptions are obviously inapplicable here, e.g. special rules for plant varieties [1] and nuclear energy [2]. The one most likely to apply to e-ink displays is that, under the Bayh-Dole act, if an invention was funded by government grants, and the patent holder fails to make it widely available, the government has so-called "march-in rights" to license it to third parties themselves. However this has never been successfully used. Wikipedia summarizes: "Though this right is, in theory, quite powerful, it has not proven so in terms of its practical application" [3].
[1] Perhaps because it's controversial to allow plant varieties to be patented in the first place, the statute for them has an explicit compulsory license clause (see the last subsection): https://www.law.cornell.edu/uscode/text/7/chapter-57/subchap...
[2] https://www.law.cornell.edu/uscode/text/42/2183
[3] https://en.wikipedia.org/wiki/Bayh%E2%80%93Dole_Act#Petition...
I mean, someone can also compel you to license your IP using a hammer.