You're going to get your account locked, banned and/or suspended. Twitter has tightened up considerably in the last few weeks and is penalizing aggressive following activity. I'd slow it down or cease completely for a little while until Twitter eases up again. This stuff ebbs and flows. I've backed my settings down considerably.
Anyway, here are my thoughts:
1.) Your followback ratio is way too low. I'm not sure about tweepi's capabilities, but you definitely need some filters in place. You need to only follow people who are active on Twitter -- say, people who've tweeted within the last three days. You might be following a lot of inactive users, and even bots, and that may be what's keeping your followback ratio so low.
When I was following 900+ a day, I was typically getting anywhere from 200 to 550 new followers a day. I now follow 100 to 200 a day and tweet some Vines or gifs each day, and I still get about 100 new followers a day.
2.) Look for accounts that are not only related to your account, but that have also used the mass following technique themselves in order to grow. Basically, look for accounts where the following and followers numbers are more or less equal. Follow their followers -- those people are very likely to follow you back, because they already have a demonstrated tendency to do so. (But be sure there's lots of activity on the target account in the form of likes and retweets -- you want to avoid accounts that have been built through #teamfollowback etc.)
3.) You can follow and unfollow in the same day. It's not a problem, in and of itself.
4.) Only unfollow the people who didn't follow you back after a certain period -- say, three days.
5.) In addition to mass following, and given Twitter's strictness lately, try for some organic growth. Find something that will get a lot of retweets in your niche -- memes, gifs and Vines are good in many niches, and plain old quotes can be good, too. Tweet this type of material as often as you can. The retweets will dramatically expand your reach and get you more followers. As your account grows, this becomes more and more effective. Also, tweet a trending hashtag or two each day, if you can think of something that relates to it.