A nice road conversion can make for a much better riding bike than an off the peg fixed gear with track geometry.

Find someone who has had experience doing this and it won't have to cost you a fortune... in many cases it takes no more than swapping the freewheel for an ss unit or installation of an ss kit and moving the chain ring to the middle to get a decent chain line.

It does not take long to remove the derailleurs and shifters.