Progesterone?

I’ve seen posts on here saying that some people’s doctors wanted day 21 progesterone above 10 and supplemented if it was lower than that. I do have low ovarian reserve. My doctor is telling me that my low progesterone (7) is due to low egg quality and supplementing wouldn’t help. I feel like more than egg quality affects progesterone and other hormone levels. My luteal phase is short, and my doctor says that’s because of poor egg quality causing low hormone levels. I feel like even with a good egg, it wouldn’t be able to implant with a short luteal phase. With low ovarian reserve I feel like even if it’s futile, it’d be worth at least trying to supplement. If the egg were defective, it would either fail to implant or miscarry, right? Has anyone else been in a similar situation? I have an appointment next month with another doctor for a second opinion but my time is running out and I’d like as much information as I can get.