Here's a real challenge...
A Ratted Survival bike!!!
Get a real non-runner and use only what you can scrounge, or perhaps find in a scrap yard.
For those readers that don't know, a proper Rat bike is one that is kept running using the absolute minimum in terms of kit and cost. Usually this results in a rusty, grubby piece-of-junk looking bike, often painted matte black all over for simple aesthetic reasons, but also some ingenious methods of repairing the bike.
For example, rather than properly weld up an exhaust hole, a Rat would just have a piece of Coke can secured tightly over the hole with a pair of hose clips, or something.
A popular cheap fix is to accessorise the Rat with military surplus items, such as ammo boxes for panniers.
Survival bikes are normally 'Ratted' on purpose for aesthetic reasons. They look like something out of Mad Max, but are often mechanically well maintained. A true afficionado will have a Survival bike that is properly Ratted.
I quite fancy doing one myself, actually!