The reason of using 2-layer pcbs is to avoid the jump wires. On a complex board there would be lots of them in all directions. Your layout doesn't need the second layer, which is simple enough to be routed on a single layer without wire bridges. If you get stuck you may have to move some components to another position, but it can be done.

My suggestion is to try it with single layer pcb instead of going the easy way of the 2-layer board. If you don't succeed in doing this on a single layer, you'll never be able to do a more complex board on a 2-layer pcb either.

Thanks for marvelous posting.