Stevie
They always try it on for the first offer. I think your collecting of evidence is the best route to explain your reasons for a higher valuation.
If you end up being seriously adrift of a reasonable price, get an independant valuation and press for that. I was offered this by my Insurer when we didn't agree. Note that the insurance company gave prior agreement for the independant valuation which was to be binding on both parties (i guess this agreement is crucial). The cost was to be borne by me, however if the valuation was in excess of the Insurance company offer, then they would pick up the bill for the valuation also.
The cars are notoriously difficult to value as condition is everything, given potential repair bills to correct a dog. Book prices are guides only (thankfully or I screwed up buying mine)
And there is an insurance ombudsman but I am not sure how he is brought into play.
Brian