... What's the outline measurements so I can start from there? mm preferably.
Slightly bigger than the PIC...
(Sorry, had to use that.)
If you are happy with your original board outline size...
1. just take your original design, rip up all the tracks to wireframe/ratsnest.
2. flip the components on to the bottom layer.
3. re-rout the tracks, using vias, to look something close to my example.
One other side issue to be aware of...
Most cheap PCB manufacturers have a minimum board size.
The company I use has a 20mm by 20mm minimum.
Your board is going to be a lot smaller than 20mm.
You may need to lay up multiples and either have the PCB fab 'V cut' your board or cut them up yourself with a scroll saw.