Didn't contact my MP but was in a similar position to you and I called them again yesterday and said I was interviewing for a job and employer requested COA - they then gave me details of who to contact but also the lady on the phone was helpful and said she could see I'd been waiting over a month and would put a note on my case to escalate it.
Honestly it's so frustrating so email your MP but in the meantime keep phoning multiple times a day even and speak to multiple people because you may get through to someone who will escalate your case (who knows why the 40 phone calls I made before that didn't suggest escalating - seems to depend on who you get through to)
Good luck
My details:
Am non-EU spouse, EU spouse was granted settled status 16 Aug (1 days after applying)
Submitted my application for settled status: 16 Aug (I simply gave my NI number and they said it was sufficient proof of 5 years residence so my case should be simple)
Biometrics: 20 Aug
COA: pending
Settled status: Pending
What frustrates the heck out of me is a friend of the same nationality, exact same situation as me but a stay at home mom therefore no NI contribution history - submitted her application and had to submit 5 years worth of evidence of residence, got COA and settled status within 2 days. I can't fathom why, when we applied on the same day, hers was approved so quickly when it was more complicated and mine is pending