I am having trouble visualizing what you are saying. I think (might be wrong) you have mixed two setups in your description.
In the typical setup being described by just about everyone here, the bungee is a small cord that goes around the next so that the alternate is just below the chin. The long hose is the primary that goes around the nexk, with any axtra at the bottom of the loop either tuck behind equipment (like the light battery case in the picture) or tucked in the waist band.
This statement of yours seems out of place with that: In that case there should not be a need to reattach it underwater.
I wonder of this statement by Devon confused you:
If you have a preference not to neck-loop the long hose (hard to have a preference until you've tried it), then you can fit some bungee cord around your tank and secure it there. That's a one-shot deal though - as once you've deployed it, you'll need to pause the dive and get your buddy to fit it back under the cords. That's how BSAC train their tech divers.
That is a very different approach advocated by BSAC and almost no one else. BSAC does not like the system described here and does not allow it. As I understand what he was describing (please correct me if I am wrong), in that case, the alternate, not the primary, is on a long hose and bungeed to the tank. I don't like that system myself, although I can only say so in theory. I have personally never seen it used.