Why not mount an NMO and use an NMO to 3/8ths adapter? http://tinyurl.com/6n8yo4w
you can add a square of sheetmetal between the roof and headliner to stiffen the sheetmetal around the mount if you needed to.
NMO mounts seem to be peculiar to the US. Here in the UK most commercial/public safety antennas are Panorama mounts. Theres no adaptor for these, and i suspect they wouldnt be strong enoug anyway.
I'd rather not use a SO-239 type with adaptor, although its an option if i cant find a 3/8th with suitable narrow clearance.
I will be including an additional sheet of aluminium to add rigidity.