Since the historical reason for installing chair rails was to protect plaster walls from being dinged by chairs, and typically only dining room chairs at that, you will not have any hstorical prescedent with your paneled walls. The first thing that I would do would be to do a lot of measuring to find an appropriate height, preferrably in the 28-36 inch high range where you had as few meetings with other moldings as possible. You do want to get the moldings so you don’t have to get them to conflict with window sills and stools. From there, you probably should be able to get by with butt joints or minimal cope cuts to meet with the old moldings.
Without knowing the size of the various moldings, it’s difficult to say much more but another possibility would be a long miter (about 25 degrees) on the face of the chair rail before you cut across the rail to end up with a thinned butt joint. Please be very careful in making the long miter as the wood will not be well supported and there is a good possibility of kickback on a miter saw making this cut.
Henry in MI