I would have the same problem and then prune my twitter follows down to something more manageable. Then I would slowly build up again and the same problem would occur. Now I just switched on mobile notifications for the follows who I really want to read everything they post, which has really just created another, smaller twitter feed.

What we really need is for the app to keep track of where you left off, cull the new posts into a separate page, giving you something easier to work with and catch up.