These items don't stack. If your consumption is, for example, 200k/h and you produce 50k/h (putting you at 50k/h - 200k/h = -150k/h), then applying this item will put you at -50k/h (= 50k/h - 0.5*200k/h). Applying more than one just cancels the previous one(s), which I'm pretty sure the game warns about.

You could apply production boost and Davy Jones' locker relics, if you haven't already, but at some point it is simply impossible to work around rum negative just through items.

What you CAN do is:

1. Kill off some of your units (on prizes, enemy Presidios/Bastions, Treasure Islands, etc).
2. Buy rum when you need to spend gold and lumber.
3. Have your BH send you rum when you need it (but this is cumbersome due to limitations and the need to be online at the same time).
4. Plan your raids carefully, so that your parties come home at the same time. That should give you enough rum to spend down.