You're choosing a realistic set of schools - I'd say that so long as your applications are well executed, you have a shot at getting into a few of them (which ones no one can predict in advance, but you should be able to get into at least one of them).
As for your story, you can't dance around the facts (the dates of your employment, and employment history - it is what it is). No way you can spin that. Best thing is just to come clean. It's not about being a PERFECT candidate with a spotless record. It's about being a COMPELLING one. And a compelling person is far from perfect. He/she certainly may have some aspects that are spotty, but he/she would also have some strong to exceptional experiences as a counterpoint.
Don't be perfect. Be compelling. If you have experiences or achievements that you feel make you strong or exceptional, then you can in a way round that out by coming clean about other aspects. Being imperfect may not get you in, but it sure gives you a better chance than trying way too hard to "spin" your way into some polished version of false perfection that just comes across as BS.