Routing VCC with jumpers?
Nothing will work as well as a 4-layer board, but if the costs are that critical then it is worth a try.  The wire inductance will be larger than a trace on a pcb layer running above a ground plane.  Be sure to have plenty of medium and high frequency decoupling as close as possible to the device pins.  Also, the loop inductance will be larger, and the wire will radiate more.

I've seen this done with miniature coax, but my guess is that the added wire prep and assembly labor would cost more than the 2-layer / 4-layer incremental cost these days.

UPDATE:  Now that you've posted the board, AND IF it is the green traces you want to replace, you can push most of them to the top side.  many of your reference designators are blocked, so this will get messy.


Starting at the far right, bring the 3.3V via left to just above C11, and route a red trace to C2x pin 1 where the via was.  Place vias above and below C11, green trace below C11, and red trace to the connector pin 2.
Red trace from the via above C11 to the left of C13 pin 2.  Via and green trace below the trace from U1 pin 4, to the existing via near C17 pin 1.  You now have two very small islands in the bottom side ground plane.


UPDATE #2.  Instead of #2 above, run a red trace from pin 1 of the large round thing (electrolytic cap?) right of the connector, to U1 pin 5.  Now the ground plane under the trace from pin 4 will be continuous, and there is only one short "jumper" on the bottom layer.