This is a JFK T7 departure. The best thing to do frankly is to go to T7 and see if they can move you on to another service. BA172 doesn't look too full (though it depends obviously what cabin you are in).

I would try using Skype on your Smartphone since that should work fine. There isn't a specific Gold line except for the UK. Otherwise the USA number is
1-800-AIRWAYS (1-800-247-9297)

You can logout of BA.com (or go Incognito) then use this link to switch country and thus telephone number
https://www.britishairways.com/en-gb...cts/contact-us