I'm playing on a server and I've got the ore quintupling set up. My base is loaded via a Personal World Anchor so that it's loaded only when I'm on. However every time I log on and go to my base I have to replace every single pressurized tube because they won't move gases.
In this picture, I've removed and replaced the tube my cursor is pointing at, but the gas (hydrogen chloride) won't go to the other tubes in the network.

I'm using mekanism version 8.1.2

This is due to how mekanism handles object loading in a newly loaded chunk. A chickenchunks chunk loader will solve the issue completely until such a time that the devs can fix this issue. It might be solveable by the method you described but it should automatically detect newly loaded pieces if it doesn't already.

Update Mekanism to 8.1.4, this should have been fixed.