I typically coat the paper, and let it air dry for 30-40 minutes. Then I coat again, and let it air dry for 5-6 minutes. Then, I use a hair dryer on low heat to dry it to the touch. As I said, I don't find that I need to use oxalic. The RH in my darkroom is almost always about 50% minimum, and will go higher in the summer. I use a timer so I am somewhat consistent about the coating procedure, and it seems to be quite consistent.
That has worked well, and the second coat definitely increases DMAX, and also improves shadow detail.
I have found that I get slightly higher contrast with COT320, but the dmax appears to be about the same. The differences between the papers is subtle. It also appears that the COT320 has fewer imperfections. I have mostly switched from Platine to COT320 because it seems to be a bit more consistent for me.