Card-swapping, I remember that as well now! In our version we could pick and choose, though - swap any cards in our hand for any of the face-up layer, rather than having to choose between one hand or the other.

Ten to burn seems to be pretty consistent - though yours is the first that I've heard of to place any restriction on when it can be used. And I'd never heard of determining the player to start, either - I think for us it was always the left of the dealer.