Mike, that carbine in the picture looks really nice from the one shot you posted. It looks to have a 1901 rear sight which should be the "c" marked carbine sight to be a later sight but can be considered correct. The 1899 carbine, if overall correct and relatively original with a good bore, can be valued at $1000-1200. They are available cheaper at times but not in really good condition.

As first asked, the headless cocking piece adds nothing to the value of the carbine. It is not considered rare.

Maybe make a lower offer if you can. Good luck!