Hi Mr Punch,
I think your last point may be more important than the copyright issue. I think that since Mr Price died in the state of California and was resident there in the latter part of his life, we need to consider the Califiornia
Celebrities Rights Act*. This protects the name, voice, signature, photograph, or likeness of a 'celebrity' for 70 years after their death, where the intended use is deemed to be commercial. This would cover the use of any of those characteristics in the advertising or endorsement of a product. However the Act makes it clear that "a play, book, magazine, newspaper, musical composition, audiovisual work, radio or television program, single and original work of art, work of political or newsworthy value, or an advertisement or commercial announcement for any of these works, shall not be considered a product, article of merchandise, good, or service if it is fictional or nonfictional entertainment, or a dramatic, literary, or musical work." I have no knowledge about the caselaw resulting from previous claims made under this Act, and so I don't know exactly how the courts have treated the use of a celebrity's likeness etc, in a work of fiction, but based on what the statute says, you should be in the clear.
Price didn't make his first film until 1938 so none of his films will be in the public domain in the US solely by virtue of the 95 year rule brought in by the 1976 Copyright Act. However it is more than possible that one or more of his films, made before that Act came into force may have ceased to be protected by copyright because of a failure to register or re-register the film with the US Copyright Office, or for some other fault, such as not displaying a copyright notice, although I would be surprised if the latter applied to any Hollywood film. I suggest you start with this
Wikipedia article. Alternatively you could use the list of films in Price's IMDB entry and cross check each one against the
US Copyright Office registrations. This would be very time-consuming. Bear in mind that any of the films Price made in the UK would be subject to UK copyright law, which generally speaking said that until 1995, copyright in films lasted for 50 years from the date of first release. In other words a film made in the UK before 1945 would be out of copyright here. However I don't think Price was making films here at that time, despite titles like
The Private Lives of Elizabeth and Essex, and
Tower of London.
*
Technically the Act applies to all residents of Califiornia, although obviously it was primarily intended to protect celebrities as they are the only people who are likely to have their characteristics used to sell stuff.