Simon,
Welcome to posting!
What to do without repainting?
Zimmerit it! 
Seriously, is it painted with enamels or acrylics? And as Darren asked, is the paint sealed prior to the weathering?
If you used acrylics or sealed it, you may be able to get away with just wiping it away with more thinner.
If not, try Mike D's idea.
Or, use thinner to dilute the streaks and work them into the paint as weathering. I understand why you do not want to obscure your good camo work.
If none of those ideas are practice or appealing, what about covering the turret with foliage and storage?
Sorry you are in this pickle. Long ago before I fully understood how paints can behave, I built Italeri's Pzr IV F-1. I painted it a glorious 3-color scheme, then used a new technique I'd read about: brown paint in mineral spirits for wash. Looked good except the next day the horizontal surfaces paint was cracked like dried mud.
Success with your fix!