Just allow your magic item destruction to bank, like others suggested. That way you can destroy things when you find them (which makes sense), and store up excess gp value of destroyed items for later days.
Otherwise, I can see carrying them around in some sort of sacred pouch or something, and performing a solemn cleansing ritual at dawn each day to destroy one item, purging it's magical influence on the world.
I also think this class should get the Dragon Blood feat from Kingdoms of Kalamar Player's Guide for free. It let's you feel the presence of magic with your bare hands w/a Search check at DC 15 for touched items, DC 20 on non-touched items within 30 feet. Each use after the first each day suffers a cumulative -2 penalty as your magic sensitivity gets blunted with use during the day.
Finally, you should be able to gain the destroy-magic benefit from destroying even magic not in the form of a portable item, such as a magically evil alter, a magic archway, and a magical trap. Perhaps even a magic-using opponant!
[Additional Note: Never forget that Mithril and Adamantine is not magical, but does give some benefits as if it were magical. A Mithril Breastplate and Adamantine Greatsword do wonders for Forsaker],