I don't recall there being any Packard-powered aircraft in any of those races.
Nope, no Packard power back then. As mentioned in an earlier post, RR could not produce in quantity, and came to the USA looking for production; this was prior to US involvement in the growing and soon to be world conflagration. Henry Ford was too arrogant and political, and Packard stepped in. At the time, the US had no such engine of such great capability. Realistically the Packard unit was a license-built engine most of which ended up on US planes.
When Packard re-engineered the Merlin, it became the V-1650. Both engines are remarkable engineering efforts. I've seen them up close on a building stand, and one can't help being astounded. They are beautiful--and huge!
There's a good book, a bit hard to find (don't know where I found it, but I did...probably at a bargain table at Barnes & Noble!) called The Fall of the Packard Motor Car Company, by James Ward--and it covers some of their war time and military contracting exploits. A sad tale of a great marque, of which the RR licensed engine played just a bit part. A good read for those interested.