Agree that the right branch from inside the bend is not an option. Even though you've gone to all the trouble to wire it I think it should go.
Interesting what can be seen or not seen in internet pics.
@SeanS sees the back branch as 'really just a shoot' but
@Hermes33 states 'rear is vigorous and way too long' That's not visible in teh first lot of photos but I can see it in the second group. In any case, probably not a keeper either if the main trunk is to stay.
Always consider if any branch could possibly replace the current main trunk. Replacing the leader with a branch is one way to get better taper.
In this case I think the existing trunk looks good. Probably better than any of the first set of branches even though it only has slight taper so I'd probably keep the main trunk and remove right and back branch too.
Remember, always take internet advice with a grain of salt. We can't see the whole tree so always check that advice given fits with what's actually there before committing to chop.