The way I tested it is as you described – by adding the brid.gy/publish/mastodon link as a custom provider in Syndication Links.
My own test post wasn’t great though – it included the link back to my site (even though I have it set not to in Syndication Links), and also included the text ‘Also on’.
When I get chance I will test it further, and maybe write a blog post revisiting all the different IndieWeb to Mastodon options!