“For my new workflow, I still manually post the same photo to Instagram and my website, but now I copy the Instagram URL and add it as a syndication link on the original WordPress photo post. […] It’s not an ideal solution but for me, it works better than the other solutions I tried.”
In general, this means that you should make posts on your own site, then copy the post to silos like Twitter, Facebook, etc., to reach the folks in those communities. To complete the process, include links on your site from the original post out to the syndicated copies.
One fun reason to do this is that tools like brid.gy use syndication links in order to backfeed comments and reactions from silos like Facebook and Twitter to your own site.
I'd been collecting these links for a while and displaying them in a "hidden" way - so tools like bridgy could see them, but a human reading the page would not.
Yesterday I added a "See also:" section that includes links out to any syndicated copies of my posts on other sites.