and most of us deal with this on a ongoing basis. Corners are never square and corners are never true two 45's.
Well, the idea of coping is a very good one and I would like you to continue with this process and more trials before the final. If you are off a bit, please, remember this is what caulk or spackle is made for. Then too, I have found that an exacto knife or sandpaper rolled around a pencil will make many of those cuts fit better. This method is the best of all. Again, as you know, one end just butts up to the wall and the other matching piece is coped to fit which is only a trace of the piece on the coped end and cut out.
Now, if this just will not work out, you can do the 45 cuts and then work the caulk and spackle to fit in and make the corners even. This will work also. you will have to let the caulk dry which cannot be sanded and then paint it, or use spackle or Rock Hard putty and fit it in and then you can sand this material down for a finer fit.
Now, you could do this also. Consider putting 1/4 round in the corners from floor to ceiling. Then mark where the rails meet the 1/4 round and knotch out that area on both sides so that the rail fits slightly into the 1/4 round then spackle this in and sand. This might work for you but you will have to use the largest 1/4 round molding made, it comes in three sizes.
Then you could modify your rail to something easier to cope and not all those delicate cuts. You might find a simpler rail more easier to cope.
Or you could get squares only and just have a butt joint in the corners and forget any mitering or coping.
Or you could take your existing molding to someone who has an adjustable mitre saw and have a bunch of different angles cut for example have 4 ea of 30 and some 35 and some 40's and have them cut in only one foot lengths. Then use them as a puzzle and fit the one that goes in the best then on the other end you just butt up the runs to meet the other corners.