Entity reference, save only value
as far as i can see there are 2 options, and both would involve writing some custom code. 

1st, provided that you have enabled product revisions, when saving the invoice, save that particular revision number and then load your product based on that revision. 

2nd, would be to add product fields that you are interested in, to you invoice (price, desc etc.) and based on the product attached save those in form validation handler