I’ve had my own struggles with getting IndieWeb working here too. I’ve a fair bit I still need to sort out.
I wish I had a bit more time to play/work with this stuff, I don’t think I’d fix any problems but I might get things here working more to my liking.
I do think that WordPress is the best chance of getting the IndieWeb working for the rest of us. The other approaches seem to technically daunting for me.
On getting webmentions to work I found the WP Crontrol plugin useful. It lets you see the webmentions queueing up and you can run them manually. That might be worth a punt.
Anyway, good luck and I’ll be very interested to see what you come up with.