Perhaps I'm missing something, but I haven't ever had to 'go over' the board with PCBWay. Maybe why they are so cheap, but I've only ever had one quality issue.

I send the gerbers and pick and place and take it from there. I approve photos If they have any question (which is rare) its over email. I don't even mind sourcing the parts/pcb/stencil myself. Its the components which make the tariff painful.