My personal thought is don't convert it, That bike looks super nice how it is. It looks new, & that you just got it tuned up, It looks like it rides really nice how it is, It would kind of be sad if that got converted, Its fine how it is. It has original parts, Its a classic, even If its not a high end bike at all.
I would say fined a different bike that's more busted up, or just frame & convert that, I mean you are just going to be striping perfectly fine parts off of this bike, keep it how it is, don't destroy the bike, If your going to be paying money for new parts why not just put them on a new frame, an actually fixed gear or track frame.
Everyone needs a good road bike.