I dont know how fancy you want a bike, but I put one together for about $105 including all the extra stuff I didnt really need, but wanted on the bike. I found an old 80s Jam|s Explorer for $25 and put a new rear wheel in it (single wall Araya rim and cheap Shizmano cassette hub). Then I had to get some new tires and a good wide riser bar. Also, a new saddle and a BMX cog were among the necessities. The rest of the stuff I have are parts that I robbed off a bike I parted out (and paid $15 for). Just search garage sales and stuff if you want to go that way.
If you are looking for a nicer, newer bike to convert to SS, then you are pretty much stuck with using a chain tensioner since most newer bikes have vertical dropouts, excluding the pricey SS specific frames. There is nothing wrong with a tensioner, but it isnt as aesthecally pleasing as a bike without one. You can find decent used bikes for well under $450, which would give you some extra spending money to do the conversion and add some schwagg.
Last, you pretty much have the Monocog as your only new option. They retail for $410. I think the next step up is something like a Kona Unit, Bianchi SASS or BUSS, or Surly 1x1, which all are in the $700-1000 range, so even finding one used will be tough in your price range.