For the next month, every time you find something interesting on Twitter, go to the source. Look for their RSS feed - if they don't have one, ask them to work on implementing one both via Twitter and via their contact form.
I don't know if it's still the case, but there used to be RSS feeds for Twitter accounts too.
And what then do I do with the RSS links? The last time I dealt with RSS at all was in the Google Reader days. Are there cross-platform solutions that maintain any context? Is there any way to reply or give feedback through RSS, or participate in conversations?
check out feedly.com its a nice RSS aggrogater website, with a competant ios app as well. Ive used it forever, and like the parent said, when I find myself on a site that provided a story I found interesting, I tried to add the host website ( like https://example.com ) as a rss source, and feedly checks and offers any rss feeds it finds.
I don't know if it's still the case, but there used to be RSS feeds for Twitter accounts too.