Adjust your goal from "Build An Audience" to "Publishing stuff I myself would want to read if it existed" and the audience will find you eventually, as long as you follow POSSE (https://indieweb.org/POSSE) and have genuine posts.
any idea how good the tooling mentioned there is? its the key to successfully applying this strategy, the best way would be to have it as a part of your blogging software/platform of choice and just working. because no one wants to do the monkey work of reposting everywhere
Not sure you need a lot of tooling unless you publish many articles per week. If you're just doing one article per month, linking them (not reposting, but sharing a link: "syndication") on 5-6 platforms would take you a couple of minutes at most.
Automated cross-posting is pretty well-trod territory.