Yep, probably your best bet. Prices on eBay are overinflated to say the least.
The easiest way to do it is find an old 70's or 80's 5- or 10-speed racer. On these the gear cassette unscrews and is the same thread as a fixed-gear cog or a single-speed freewheel. Simply get your local bike shop to swap it over and re-space the wheel if you can't do it yourself
That age bike is most suitable because the rear drop-outs are usually long so you can set the chain tension. 6- and 12-speed bikes can be used but don't always have a screw-on cassette because some of them are splined.