OK, I will spin another board with traces on the outer layers. It'll take some time for the trace routing and optimization.

I did a quick estimate at easyeda.com to get an idea of what 5 PCBs would cost. It was a surprise to say the least.

5 PCBs, 4 layers, 244mm X 305mm with shipping is right at $200. Yikes! The same order last year for 2 layer boards cost $70. Going to 4 layers really boosts the unit price up. That's a unit cost of $40 which is higher than my previous guesstimate. More units would probably bring it down though if more people got involved.