You could just carefully design your PCB so that all connections between sides are "straight" and then you can use jumper wires.
I use something like this for my double sided boards. Place as much as possible on one side, then the few traces on the other side are all straight lines. Do the standard toner transfer for the complex side, use those itty-bitty otherwise useless drills in the cheap drill set I got to drill through the vias to mark the back side, and connect the dots with an etch resist pen (actually, I like a fine paint pen a lot better than an etch resist pen, and they're easier to find locally). Etch as usual.
-j