As for Twitter’s other functionality… I have, in the past, declared Twitter bankruptcy, unfollowing everyone and then refollowing. It’s harder than it used to be in the past, and I don’t necessarily want to lose track of anyone I’m following right now. So for the time being, I’m noticing when I do browse Twitter which accounts I am finding most valuable. Then I’m using TwitRSS.me to create RSS feeds of those accounts and subscribing to them in Feedly.
If you want to know who I’m following, I’ve got a page for that on my website.
The other key functionality that Twitter has for me is the use of hashtags to aggregate posts about conferences or on Twitter chats. For those purposes, I’m using Tweetdeck and creating a column for each relevant hashtag. My likes and retweets will be posted from my website and then syndicated back out to Twitter.
If you mention me on Twitter without replying directly to a tweet of mine, it should still ping me on my website. I’ve got a special page for Mentions. It’s not linked where anyone but me can see it without typing the URL in directly, but you can trust that I will see it.