It does seem a little awkward doing an overhead join coming from the dead side.
Not at all. Route to the overhead and orbit in the direction of the circuit until you have seen all the traffic and then commence the descent via the deadside.
People seem to think that you have to descend immediately on reaching the overhead. Not so, you only descend when you are ready and can slot into the existing traffic safely.
As for people who say, 'oh just I prefer to just join this way or that way' perhaps they would benefit from some revision and airmanship!