The British papers would be the place to look if they referred to the battle as happening at Staten Island (rather than Long Island) - if not, I'd be looking at colonial American ones.

Either way, there is good chance that an assembly that introduced a new dance in commemoration of a major event like that would have been advertised in advance or reported in the equivalent of the society columns.

I'll be in London in November and might have a chance to look in the British Library, if nobody else gets there first.