Hi
to answer the question not an easy task, (I know that quite well with the research work I did); so, since there no definitive answer on how the Soleil Royal would have ''exactly'' looked like in the spring of 1671 when it was being prepared for the king's trip, here is what I found in relation to the Tanneron model. First, the hull itself is only a ''vehicle'' to support the decors on the bow nd the stern; it's shape, not considering the upper rear planking (in black) would be quite close to the 1693 Soleil Royal, the real second one; the dimension are quite a bit closer to that ship than it is for the second one. So why use that? because Tanneron had the plans for the scond ship, which by that time were mandatory for the naval archives. The decor is the description of Puget's drawing which is stored somewhere deep in the old archives at the naval museum of Paris, or depp in the archives of the Louvres museum and it carries a number between 691 and 695. I still haven't found it and will need to go there to dig..... The rear facia could be considered very close to what the first Soleil Royal looked like, so did the front part.
As for the side galleries or ''bottles'', Tanneron had the description of the decor, but didn't have the sructure description or the dimensions so he most probably refered to the Louis XV model at the museum, the only model which was made in the 1720's and refurbished a few times since. If we look at the shape of the side galleries from the Louis XV and compare, the similarity in the overall shape comes into view.
When the ship was rebuilt, the decor was altered, the statue became a bit smaller, it now had 6 instead of 5 rear windows because it had been vertically straightened and somewhat lowered a bit, which is reflected in the rear main board decoration.
In a summary, the story goes like this; Le brun drew the first iteration of the decor; Colbert changed his mind after the Royal Louis and the Royal Dauphin were built, and contracted Puget to modify extensively the stern's decoration to make it lighter and with less full busts statues which would create ''hooks'' in battles for fire ships; and it had to be ''in very good taste''....
With what I have researched, The Tanneron is an execution of the Puget's stern and the Lebrun bow decors; the side do not have any specific decorations as there is no description of them. The hull is the dimensions and the number of canon ports the second Soleil Royal would have had in 1705......
I hope this answers a few questions, and there are more, I'll be glad to answer to the best of my information...