I'd use a "power-up" item AND a "actual" item. You can pick up a "rune" or "gold chunk" with full inventory, so if you base it out of that, you can ensure it's possible to pick up if full inventory.
But, if the effect should not be now, and you need to keep the item, you will need to make it to the "actual item". Whenever you drop it, you replace it with the "power-up" version.
That'd be my solution.
It's not great because you will need 2 items for each item and switch them out back and forth, but it should work.