It shouldn't affect it unless you use X-Zone or Break instead of Doom to kill them. A better strategy is to use Relm with the Fake Mustache Relic to Control the Brachiosaur and just use magic on it so it stays in Control status.

The Celestriad/Economizer is a rare drop but you can steal Ribbons from it. Also, the Aquila enemy in the Phoenix Cave has the Economizer as a rare steal item, if you want to go that route.