How do you invite clmates to your child's birthday party?

My daughter's birthday party is coming up soon. I have reserved the venue and space is limited, so I can't invite the whole cl. I didn't think this would be a problem since my daughter has gotten invitations that the teacher sent home in her bag or folder and I figured that could be done discretely. Then my daughter told me that she can't bring invitations to school unless she has enough for the entire cl. Okay. So I emailed her teacher to find out what the policy is and how things are usually done. It's been a few days and I still haven't heard from the teacher, so I called the school and asked what the policy is. I was told that invitations can't be handed out in school. I asked if I could get addresses so I could mail them, but ofcourse, they don't give out that info. It's not like I can just meet the parents before or after school, because some kids are dropped off and picked up a few hours before or after school, and some ride the schoolbus, so their parents are rarely at the school. I was told that I could have my daughter get the addresses of all her friends herself. My daughter is in kindergarten! They're just learning to write! She did write out the names of the kids she wants to invite, so maybe she can manage to write down all of their addresses too, or hopefully the kids can spell the street names out for her. I guess that can work, possibly, but my next question is, when is she going to have time to do all of this? Certainly not during cl time. I'm sure they can't bring pencils and papers to recess or lunch, and even if they could, wouldn't going around and getting the addresses of a few select kids be more distracting and seem more exclusive than discretely having a teacher or para slip a sealed envelope into a few folders or backpacks? I'm really frustrated by this because it didn't say any of this in the student handbook. All it said was that they don't allow birthday parties in school and you can donate a book instead. Maybe I could have planned ahead if I had know there would be all these restrictions. Any suggestions on how I can quickly get the addresses and mail these all out before the end of the week?