So, we attempted to make a Red chicken from description only... well, that and recipes for other colours and available information on food colours of the time. In the end, the one thing that was safe and readily available to us, ended up being pomegranate which reduced into a lovely deep red syrup but quickly turned into a deep brown with any egg yolk, or even white, added it to it.
Why add the egg? Well, yolk is mentioned with the other colours and it was not unheard of for other savoury food glazes and this is likely because of the type of glaze it forms. The egg also helps glue the colour to the surface... it isn't quite paint but a thick syrup without that added protein, would just slip off of most foods.
In the end though, with some playing around, I grabbed some cherry syrup (that was made at an earlier date) and topped the reddish-brown hen with it which made it a bit more red in colour and also decided that we need to use as little yolk as possible as not to muddy the colour.
One issue to be aware of, however, do let let the bird sit in an oven too long (something very avoidable when working with a spit in plain sight) as the sugars in the glaze will burn easily and then you will have a black chicken!