I do something similar to the OP, but there's an additional critical hack - you have to sort your Unreads view (cmd-shift-A) by the order of the channels in your groups, which is not the default setting. Then, when you you hit cmd-shift-A, you pay close attention to the initial messages from the channels close to the top (i.e. the stuff that requires your immediate attention) before hitting Escape to mark them read. Eventually the Unreads view starts to show you bullshit that you don't really need to pay attention to, and you can basically spam the Escape key to mark everything read, after maybe skimming it slightly so you see there wasn't anything of interest. Also, be pretty aggressive about muting support channels where you're not among the group of people expected to provide support.

This makes Inbox Zero in Slack easy and I don't understand why it's so difficult for other people to do it.

(currently working in a Fortune 500 with membership in probably thousands of channels, only maybe 20-30 of which are actually relevant to my daily work).