The whole idea behind IndieWeb is that you can use your website to own all your content on a domain you own/control. You’ve got a site with webmentions set up, so we could be having this whole conversation from site to site. Instead, I’m choosing to syndicate/POSSE my replies from my site(s) to Twitter, to meet you where you’re currently at. Integrating my site with Brid.gy allows me to get your responses from Twitter back to my website. Here’s some more on threaded conversations between WordPress and Twitter that may help frame what you’re attempting. (It also includes a link of WordPress to WordPress or other site conversations as well.)