I'm far from being anywhere close to knowing what the heck I am doing with this stuff, here is what I did with mine when they looked like that.
As soon as they cooled down enough to hold in my hand, but were still warm I tossed them right back in the bowl for another tumble and then into the oven to cook. What didn't get it the first time as sure nuff done up the second time.
Now, that said, I might be working on this for a completely different end result than you are so your one tumble and cook might be what your looking for. For me however I am looking to be able to run some pretty darned soft alloy (comparatively) to magnum velocities mainly in order to use my HP's for hunting purposes.
Once they come out of the second cookdown they air cool and are sized using the Lee sizing die. I have however decided that with the batch I am cooking right now they will only get one coat period. Once done there are 50 that will also receive GC's as well as 25 that don't. Both will be run against one another with identical loads of 296 to see how they preform. If I see either has issues we will try it again with a double coat just to see if that helps, but if not I see no reason to coat them as the standard lube method has worked well with these bullets in the past.
So again your reasons may or may not be the same but a double coat does clear up any unsightly spots.