I experimented with a fixed gear bike last year, and sold it after a few months. Truth be told, I miss it and plan on building another one someday.
What I would do to that PX10 would be to simply redo the brake cables/housing/bar tape, and buy a cheap fixie wheelset online. Save those tied/soldered jobs for when you do a complete restoration. Something like these wouldn't break the bank:
http://www.ebay.com/itm/New-Weinmann...item3f2a0c153d