Good to see you are continuing on this one!
I would also airbrush after construction.
But I would do the contrary: use very low pressure and thin the paint very much.
This way, you can apply very thin coats of paint. You will need many quick passes (15 to 20 or so?) to cover completely, but exactly this allows a lot of control and prevents you from drowning the detail in paint.
Start with airbrushing the most hidden areas and the most awkward angles. While doing that, you will automatically apply some paint to the adjacent areas too. Then airbrush the rest.
An added benefit to low pressure and high thinning ratio is that the final coat of paint is very thin and smooth.
Cheers,
Marijn