Folding fixed gear hack

I have changed the plan for this bike.  The Bike Friday below was the best idea, until I found out that the chain will fall off on every fold, as the hinge is inside the rear triangle.  Not to mention that the $1500 cost will go up to $2000 once it is shipped to Canada or Japan, and hit by shipping and tax and duties.  And the S3X hub?  Seen a video and it has far too much lash.

Altering a $350 Dahon Speed Uno will work best, for the following reasons:
- the chain won't drop off on folds
- the wheelbase is comparatively long for a folder, and I can put the rear wheel at the far end of the dropouts
- the frame is steel, though not the fork
- the cost of the whole bike is no more than the value of the frame to me
- it folds as small as anything else
- with all the alterations, still well under $800

So what does it need?  All of this in black to be my 'Smell the Glove' bike.
- the silly coaster rear need replacing with a 20" fixed/free wheel
- 14T cog and 16T freewheel
- the flat bar needs replacing with road drops, black cotton shellacked tape
- a Gran Compe Shot lever, since I'll only run the front brake
- I have an old black caliper brake I can put on the front
- I can use this to get the seat back if needed, and this to get the bar forward, as I am 6'+
- spd pedal
- a black leather Brooks B17N or Swift Saddle
- with the brake lever on the flats for riding among traffic, I'll need dummy levers for riding in the tops

Old Post:
This is a project I have had on my mind for some time as a fixed gear bike I can take on/off Tokyo and Toronto trains, which also has a climbing gear.  Other than having the Sturmey Archer S3X hub, it would look much like this.  Yes, I know folders look silly, but larger wheeled folders are not an option on moderately crowded trains; on fully crowded trains no luggage is an option, but my commutes are downtown outwards.

The Bike Friday Pocket Rocket option is overpriced at $1500, but there isn't really anyway to beat this 'custom assembly' price, since nobody's making a stock fixed folder at all, much less one with the Sturmey Archer S3X hub, drop bars, and a steel frame, with choice of stem and seatpost length.  Some have had Bike Friday make them a fixed from the Tikit frame, but 16" wheels are just silly.  20" are silly enough, and replacements are easy as BMX uses these.

There are few other folders with the track ends needed for a fixed gear hub, whether the S3X or standard.  There are fewer yet that are steel, and there are even fewer that are affordable.  None come stock as fixed gears, which means changing components, which quickly becomes as much cost, and more trouble, than a 'custom assembly'.  You could start with a Moulton, but that's stupid-money.  The next best option is a Swift Folder, but it doesn't fold nearly small enough.  The Dahon Speed Uno is a cheap start, if you can find it, but the components it starts with are crap, so nearly everything would need changing but the frame: expensive and troublesome.

Tomorrow I find out if I get the new job in Tokyo.  If so, I sell my regular fixed gear and order the Bike Friday.  Fingers crossed...