Well firstly I would love to know more about your workflow where it actually broke etc. because I feel like tmux-ressurect team could help or something for sure.
I haven't used the tool itself so I am curious as I was thinking of a similar workflow as well sometime ago
Now please answer the above questions but also I am going to assume that you are right about tmux-ressurect, even then there are other ways of doing the same thing as well.
https://www.baeldung.com/linux/process-save-restore
This mentions either Criu if you want a process to persist after a shutdown, or the shutdown utility's flags if you want to temporarily do it.
I have played around with Criu and docker, docker can even use criu with things like docker checkpoint and I have played with that as well (I used it to shutdown mid compression of a large file and recontinue compression exactly from where I left)
What are your thoughts on using criu+docker/criu + termux, I think that it itself might be an easier thing than k3s for your workflow.
Plus, I have seen some people mention vps where they are running the processes for 300 days or even more without a single shutdown iirc and I feel like modern VPS providers are insanely good at uptime, even more so than sometimes cloud providers.