Need Advise - MBA Trader to PE

I need advise, I graduate in 2015 from a top 10 international MBA and have since been trading (non prop) at a BB. I have been applying to PE firms as much as possible and receiving little to no responses. Closest was a firm that responded when I applied to an Analyst level position. The reason for rejection was that my MBA meant that I was not fit for the role, due to past MBAs searching for other opportunities after their first years. My current plan is to respond and ask to be reconsidered given that I think that the Analyst role is better for me. My prior exp is all entrepreneurial. Not sure if it is worth going over HR and contacting the MD directly or if I should insist with the HR person who said no.

Has anyone with an MBA had experience being hired at the analyst level vs. the associate level?