My usage is similar but I follow about twice the number of people. To keep things manageable i.e. consume twitter in about 30 minutes/day, I wrote a small chrome extension to rearrange my feed (sort by likes/retweets, give different weights to users and sort the feed/list).
I wrote a chrome extension to solve something similar i.e. filter out by keywords and then sort my timeline to see popular tweets that I shouldn't miss.
Somewhat related : Wrote a chrome extension [1] to reduce some noise on twitter. It should be easy to add the ability to filter out tweets by keyword (I'll do it probably this weekend if it is useful).
https://chrome.google.com/webstore/detail/hackybird/ddlhmpom...