I recommend contacting Snow Lion Tours. They are a Tibetan owned agency that offers competitive prices and great customer service. They can work with you to design the itinerary that you want to do. They can arrange a trek for you and then have you continue on the Friendship Highway to Everest Base Camp and the Nepal border.
On the Nepal side of the border, there are buses and private vehicles leaving all throughout the day to Kathmandu. There are plenty of vehicles to get you to KTM.
I would start arranging your Tibet tour before you arrive in Chengdu. It will probably take you a little bit of time to research your route and fine tune it to exactly what you want to do. Once your permits have been issued, only minor changes can be made to your itinerary. You will not be able to add additional destinations so make sure you are 100% sure on the places you want to see. If you arrange everything before you arrive in Chengdu, that will free you up to do the things in mainland China that you want to do without having to spend time with your Tibet trip arrangements.