The answer is that you can't and shouldn't care (about ink levels and monitoring). Simply ignore ink monitoring since it won't work anymore. HP guesses at ink usage anyway, keeps a page count on the chip on the carts. No reset of the chips available as far as I know. All you need to do once in a while is to hit the OK button on the front and keep on printing. You probably already know that though.
I have the "refresh" of your printer: c410a. You get to print on CD/DVDs and I don't. I would not keep the HP monitoring software on the machine either, personally I see it mostly just a vehicle to sell you ink...