Would it be worth it? It wouldn't be worth it to me, but then again, I already have a track bike. The question is, would it be worth it to you?
Granted, you won't get stares because of the uniqueness of your ride. A 1200 just doesn't invoke the same kind of lust that a colnago or a 3rensho does.
In order to convert the bike to a fixed, you would need a new hub, spokes, rim, and a rear cog. That is 200 at the least. You could pick up a conversion or a track bike for a little more than that, and you have another bike. That's not a bad thing.
Singlespeed, on the other hand, would be far less costly. You could do it for less than 30 ( new chainring bolts and spacers on the rear) Use the RD as a chain tensioner. Remove extra parts.
In summary, fixing it would cost too much to make any sense, but SS would be justifiable.
The dropout spacing will work, and don't worry, the eno will bolt to everything.