How to keep containers (barrels) from resetting?
Solution 1:
The only way to keep containers from resetting is to personally enter the cell they're located at every X days, where X is the respawn period of the cell, sans mods. I doubt there's a mod that targets those particular barrels, but if you're determined to use them, the Creation Kit allows you to change the properties of containers.
A much simpler solution would be to use the console command "player.modav carryweight 1000000" to give yourself enough inventory capacity to carry all the things, could also be handy for relocating the stash to a safe container.