Reapplying to Master's after failing out

[Matrix21]

Hello everyone, 

I am reapplying to a top 30 program where i failed out because I didn't meet the core courses GPA requirement, I was given probation numerous times and then asked to retake a core class and get a B+ or higher; I fell a few points short on the final and ended with a B so I was removed from the program. This was in May 2017, I applied again for Fall 2018 but was rejected, I'm currently doing my application for Spring 2019 semester. Also applying to it's sister school that will allow me to transfer my credits (18-21 credits).

What's the best way to tackle the Statement of Purpose essay? There's also another optional essay to explain why I'm now a better candidate than my previous application.

I have been working at a startup as a contract developer for 6 months, now moving to a full time role at a big government organization as a software engineer. I also have a 6 month internship on my resume, a 1 month fellowship, a few projects (some ongoing). My GPA was 2.86, undergrad was 3.2 and major GPA was around 3.35, GRE is 156/158/4.0. I have recommendations from a professor at this school, a professor from my fellowship and a manager from the internship. What do you think my chances would be? I think it hinges on my essays but I'm struggling on how to exactly word my improvement and not seem desperate as well. 

Hope some of you can help me out

Edited September 25, 2018 by Matrix21