Moving products from one page to another

I've got products in a page calleds 'bows' which had a collection of bows for different instruments. I have now created three different product pages called 'Violin Bows', 'Cello Bows' and 'Viola Bows'. I don't want to have to make all the products again, can I move the prodcuts from my current generic 'Bows' product page to their specific instrument product page?

I'm on 7.1, can't seem to work out how to do it.

I also used to use this feature frequently. It's frustrating to me that it seems to have been removed in 7.1, leaving us to have to manually create duplicate product listings from scratch across the various sections of our sites...