The problem is always going to be the lens extending for optical reach. Either you have to have a permanently extended lens to accommodate the required focal length, or it will have to extend when used at the longer focal lengths. To me it sounds like a bridge camera is going to be the best compromise, and it will always have to be a compromise. One advantage of the bridge cameras is the relatively small sensor size, with it's high "crop factor". A good superzoom bridge camera with an approximately 5 to 6 times crop factor is going to give you the same sort of field of view as a 400mm on APS-C or 600mm on 35mm, but with a physical 100mm lens focal length.
I have a Sigma 28-300 lens which for the focal length is quite compact. even so it still extends to be about 12" long at 300mm, although at 28mm it is about the same size as a normal range APS-C sized zoom (a little fatter than my 18-55 but about the same length). The Tamron 16-300 is about the same size, both at the wide and long ends. So you could use one of those on an SL1/100D, for a discrete ish camera lens combination with an APS-C sized sensor, but it is till going to be quite noticeable at the long end of the zoom. The bridge type camera will likely be smaller than this as it is only having to go to a physical 100mm or so FL.
I cannot think of anything else that will give him the long reach that he will want. Anything over 300mm on APS-C is going to be big and noticeable, and getting to a physical 600mm FL is going to give you a lens that is 5" plus in diameter and three feet long.
Unfortunately the physics constrains the size that the lens has to be. Fancy glass can help a bit to reduce the size of a lens, but it is still the physics that limits the size.
Alan