I don't think it's uncommon for certain personalities to have meltdowns at their birthday party or other major event. Some kids get overly excited and can't handle things. I'm not sure even a low-key party is the answer.
My SD has had some kind of meltdown at her birthday party and other major events every year until she turned 10. I think she would get overwhelmed with the attention, the sugar and the anticipation of the party. One year it was the games (she didn't win the prize she had been wanting), the next year it was because the kids weren't listening to her (she was being bossy), another year it was because she wanted the party to last longer.
She's had major meltdowns on Christmas as well, I think she's overtired (from not sleeping the night before because of excitement) and overwhelmed with all the gifts and stimulation.
I don't think that the parties were necessarily about you, I think that you just need to talk to your daughter about your expectations and what's going to happen. Have a frank discussion about what some of the kids might do and how you're going to handle it. For example, we open gifts at the party, but she is not allowed to open the boxes or play with any of the gifts until after her friends have gone home. This keeps pieces from being lost or gifts from being broken. You may need to remove her from the situation if she looks like a meltdown is imminent.
I don't think you're alone in having a child that gets overly excited and may have meltdowns at her party. Don't let it be a reason not to have a party, and don't feel like the party failed because of it.
When we look back, my daughter doesn't remember any of the meltdowns. She just remembers she had fun.
Good luck!