Ok, I'm trying something. I've mentioned that I'm not reinstalling Twitter on my phone. So I've built a little Heroku App that emails you tweets from people you don't want to miss a tweet from. It runs once a day, and returns just plain text tweets with as little formatting as possible.
It's setup as a Heroku one click deploy, so you should be able to click a button in the readme and deploy your own version if you're interested. Feature suggestions and tweaks welcome.
https://github.com/icco/tweet-today
It's not complicated code, so hit me up with pull requests or issues on Github.
Cheers,
/Nat