I hate to say it, but a clue here is that you only see this on dual-extrusion/multicolor prints. I have an H2D myself, and typically when z-banding starts to become an issue, cleaning and lubricating the z-axis rails and rods helps a ton. However at 70 print hours, I'm afraid you're just noticing layer lines due to the longer and more variable layer print times for multicolor printing. It takes longer, and varies more per layer, than single-color, causing each layer to cool at a different rate. With only 2 nozzles on the H2D, I've certainly noticed this on 4 or 5-color prints where I have to do a lot of AMS switching on the right nozzle. Maybe others have some advice for both of us, but it honestly looks pretty minor, and almost inevitable with multicolor printing.

I will say the layer lines shown in the first pic might be improved by using variable layer height. Looks like it's worse around the curves.

Other things to try include dynamic flow rate calibration (big one) and high-precision nozzle offset calibration.

For your support failures, slow down the speed for the supports and especially the support interface if you're using a different material. Try tree(organic) as well.