I am inclined to suggest that the tinny rattling sound upon acceleration is the result of a loose exhaust system component. One of the rubber mounting pieces could be worn (ref #8-10 in the diagram below) and is causing excessive play in some of the brackets. Additionally, one of the floor heat baffle plates (ref #24-26) could be loose.
Try inspecting these components and ensuring that they're all still in proper operating shape
*diagram courtesy of hondapartsnow.com; all rights reserved