In my 34 years of automotive engineering, I have never seen a seal that did not have the small end of the rubber seal cone in the direction of the oil that was intended to be retained in the reservoir. That normally means that the flat metal part of the seal is opposite the retained oil reservoir (gearbox). In this case, what makes the installation difficult is that the seal is not installed in the transmission case, where the oil is, but in the end cover. The way you show it is, in my opinion, exactly correct. Installation should require a really thin wall tube or, better yet, the old seal with the rubber removed, butted up against the new seal outer diameter end.
Andy, please remember your front steering idler arm seal installation. The BBB described the reason for the direction of its installation. It was installed so that the grease could escape if too much grease caused the pressure in the "idler arm shaft housing" to get too high as the shaft screwed itself back and forth in the housing. Installing it in the opposite direction would have trapped the pressure in the housing and caused the seal to rupture (like mine had).
In your transmission situation, there must be something other than the seal that is not right. Trust your instincts and keep looking.
By the way, your experience has convinced me to leave my gearbox alone and live with the occasional weak synchronizer.
Good luck.
Tom Kizer