That's why "kind-of-work".

I vaguely recall that Linux has support for multiple tiers of paging space, with you able to assign priority.

googles

Yeah, swapon has a -p parameter`.

https://linux.die.net/man/8/swapon

-p, --priority priority
    Specify the priority of the swap device. priority is a value between 0 and 32767. Higher numbers indicate higher priority. See swapon(2) for a full description of swap priorities. Add pri=value to the option field of /etc/fstab for use with swapon -a.

So you shovel the priority below your local paging space, might be okay for some workloads.

I dunno if there's any system to predictively migrate data between tiers of paging space, though. If it only pulls into main memory from low-priority paging space and does so a page at a time, that's gonna be painful.

Also, this definitely increases the security risks associated with having sensitive material being paged out beyond the usual "someone might get your laptop and look at the paging space when it's off if the paging space isn't encrypted and you're using software that doesn't lock security-critical data in memory" stuff.