I have the ivory chip with this design, too. A variation of the design is said to have been used by the family of President Zachary Taylor as a crest, the emblem above a coat of arms, not the arms themselves. The President himself, however, does not appear to have ever used the crest. The only illustration of the crest I have found is this modern drawing:

The translation I found for the motto is, "He achieves what he attempts," although I will leave that to the more Latin literate.

A seal-ring belonging to a seventeenth-century Louisiana gentleman named James Taylor also shows the crest.