What month to use for birthday?

I just went through a nonviable pregnancy. Based on LMP, the due date would have been the very end of August. But based on my hcg in the early weeks, my doctor thought I was actually not as far along. My due date would have been early September based on their early estimate of how far I was based on hcg. I didn't track bbt that cycle so not sure when I ovulated, but I believe I did ovulate pretty late. I never made it far enough to get a dating ultrasound or an actual due date from them.

I want to use the birthstone for something to remember my lost baby and I'm just curious what month you all think I should use.