It looks like a very short tenon to be honest - more like a bolt-on acoustic, but without the bolt! It would be feasible in that respect to enlarge the mortice and get rid of those (what look like) two pieces of wood stuck in there and drop the mortice back 1" towards the neck pickup cavity. You can make the tenon longer and more secure in that respect. The weakest point will be the tenon and the neck as it's an endgrain join, and a dowel will only help marginally IMO. I view dowels as being better for locating and helping make a better glueing joint as opposed to for their mechanical strength (which they do provide but not as much as a good clean join anyway!).
Am I right in thinking that a dowel was located from the neck pickup cavity down into the tenon? It wasn't such a bad idea as it might seem, as the relatively small tenon looks like a bit of a weak design to me.
Given the size (or lack of!) of the tenon, i'm surprised that the fingerboard hasn't started to seperate from the neck....the pressure seems as though it would have been applied where the fingerboard joins the neck....I would definitely be tempted to get the fingerboard removed and rout a tenon a 2"-3" deeper into the neck, and 1" deeper into the body.
This is one of Ant Setchell's tenon pics:
If you imagine that the tenon is a seperate piece, but extended into the neckan inch or two, that is your ideal world target but it depends on whether removing the fingerboard is more hassle than you're willing to put up with :-/
Best of luck - I hope whichever repair option you choose works. Any more pics of the bass?