How to allow students to work off-line, while still using an LMS to collect work? Due to Covid-19, I am having to switch to a "hybrid" format, where I see students less often each week, in smaller groups, and more assignments are pushed on-line. The school is in an extremely rural reservation, where those students who live off-campus are unlikely to have running water, electricity, and internet access. Students are issued Windows laptops.

The current solution is to create assignments in Word, have students download them on campus, work on them at home, then upload the assignments when they are next on campus. I am trying to find a more sophisticated solution for "syncing" their work though, as this step makes it much more time-consuming to grade work. With an LMS, I can post multiple-choice quizzes and other types of interactive assignments, e.g. videos they watch and respond to. Is there some technology that allows for students to save specific LMS pages locally, work on it off-line at home, then when they return to school, they can easily submit? I know students could just leave the browser window open and put the computer to sleep, but that seems risky and students could lose their work.
I suggest that you use git to synchronize documents.

If assignments are provided as simple text documents, they are easily readable on all sorts of devices, and when printed can easily be understood, they can be edited with very low levels of computer hardware and do not require many resources. They can easily be edited with something even as simple as an alpha smart or electronic typewriter! Word Documetns will work with this scheme but it makes the storage requirements (on your side) larger and harder to manage

When at school, a student uses git to "clone" the asignment repository. 

When they go home they then work in their own sandbox, and are free to save ("commit")  intermediate versions, locally, on their computer, as many times as you want. They can start from scratch if they wish multiple times without affecting the integrity of the assignment and their other attempts. 

When they return to school, the student "pushes" the assignment project to their personal repository. You can review their work and can even examine intermediate versions that show their work and thinking, 

The commits have timestamps so you can verify assignment, test, and quiz submission times! (This can be "hacked" but it requires cheating behavior and intentional circumvention)

This is very reminiscent of what we I used for CS courses in University, all of our coding assignments were submitted through a UNIX shell

There are many services that provide Git for free or low cost, Github from microsoft, atllasian bitbucket, and gitlab are common examples.

They can also be deployed , for free, by your school IT on any available server infrastructure. 

In a pinch, the students can even synchronize directly to your laptop or other computer, that is, not requiring ANY LMS infrastructure...

Students can even synchronize to/from another student, i.e. you can submit assignments for others and distribute assignments as well, so students who cannot make it physically to school can still get the assignments from their peers. While retaining integrity of the assignments and solutions 

There is a significant training challenge, but the tradeoffs are worth it, and the solution is Free, free as in no cost, and free as in freedom (see free software)