HSA won't happen, to a significant degree, in the pump or heat exchanger. You need air in order to oxidize, and the pump and HX should be full of wort and sanitizer, respectively, at that point. I don't think there are legitimate HSA concerns with utilizing a whirlpool either. If there were measurable DO issues during knockout then at least the more adventurous breweries would be trying out alternatives. AFAIK no one *isn't* whirlpooling commercially.
Anyway, 30 minutes is a good starting point and pretty typical IME. Homebrew systems might require a little more time (mine does) because of using flat-bottom kettles; a dish or shallow cone is optimal for whirlpooling. I would try getting it started with a clean spoon (not the mash paddle!), then recirculating for 10 minutes through the pump only, to keep solids out of the heat exchanger. Then a 20 minute rest, drain the lines (again, solids), and knock out through the HX.
As far as covering the kettle, I do. If there are DMS issues at that point, it's because you aren't boiling long enough, and anything that drifts into the wort may not stop hot long enough to be pasteurized. I actually put the lid on about a minute before flameout so that it does get pasteurized.