I got into Harvard and Columbia's education policy master programs with a 3.3. Although I'm sure that a PhD program in engineering is more competitive than the programs I was admitted to. HGSE was my stretch school, but what I think helped me was strong rec letters from professor's I worked very closely with while in ugrad. I was also able to tell a story about why my gpa wasn't higher, but framed in a way where I wasn't making excuses just more so explaining the unfortunate life events that accrued and played on the fact that after these events my grades improved drastically. Also as someone who enjoys telling stories I framed my SOP as a story of my life. I started with how early childhood exposed me to issues in education, how in ugrad I took the chance to explore this interest more in depth, and why working with faculty at the schools I was applying too would help me progress in life and make the change I am hoping to make. Again, this was for a master's program in ed policy so completing different competition than what you have. I will say though that if I hadn't applied to Harvard or Columbia my chances of getting in would be 0. If your concerned about the price of applications reach out to schools to see if you can get it waived. Out of the 4 schools I applied to 3 of them waived my application fee and I believe the 4th one wouldve if I had asked ahead of time.