Little issue in hgschmie's version: if move a tank of fluid with the new version, it empties the tank, which is exactly the reason why I wanted to use picker dollies to move it (same thing for pipes).
Luckily, Factorio 2 doesn't seem to make you lose any fluid, if the fluid network has enough room (so you can build a new tank at one end, and remove the old tank without losing any fluid now, this used to only work if the tanks were directly connected).
From what I understand a similar feature was added to 2.0?
https://factorio.com/blog/post/fff-402
That's only for preserving the wire connections, it doesn't work for contents (when you want to move a chest, machine, or tank).