I have done a fair amount of dyeing with Eco Flo water colors and have run into the same thing. My best results are after I let the piece dry for at least 24 hrs preferably 48. I'm in S Texas and it can be quite humid. I then buff with a terrycloth or wool cloth to get any excess dye off the surface. The first coat of finish ( I use Super Sheen) is applied with a wool dauber and extremely light. A small pump bottle mister also works well. Again dry dry dry. 2nd coat is heavier and the the finish should be complete.
Really cheap hack for the rivets is.. I use a grade 8 bolt from the hardware store--I keep a 5/16, 3/8,7/16 and 1/2 bolt handy. They have a cupped end on the thread end of the bolt that is pretty close to the curve on those domed rivets. Unfortunately it does not work for double capped (rivets with dome caps on both ends)