Oh boy, BTDT! Melmo, I understand the dilemna. We lived 4 houses away from the school -- 3 if you don't count ours. 2 of my 3 kids went to that elementary school for all 7 yrs, and thusly we knew every kid in neighbourhood, as well as being the unofficial landing place for all my childrens's friends and the yard everyone played in.
Hence: There was no keeping anything much of a secret. Everybody either knew everything, or walked to school w/someone who did.

We thought we were subtle:
We got class directories every year, & sent party invites via snail mail midweek. However, inevitably By Monday some kids would come to class trumpeting "I got a birthday invitation from______!!" Yeesh. sigh

We sent b-day cupcakes for the whole class plus teacher, principals & aides. lol
Unless you're truly prepared to have 30-ish kids rampaging thru your home & garden, it's just not possible to avoid the "Exclusion trauma" sitch.
It got a lil better in the 4th grade or so; the children started breaking along gender lines so far as b-days went; ie sleepovers for the girls only; video game arcade craziness etc for sons.

Prob I went overboard but my kids had 3 b-day parties a year until high school: Party w/school friends. Party for Grandparents, cousins, & assorted family. Party for friends & associates (from gymnastics, fencing, dance,orchestra, w/e) who were not classmates. Ouch my aching back & overworked baking implements. ha

It can be awfully bumpy, but the fact is: Not everyone gets included every time. Not every player wins at every game. Not everyone makes the honour roll. And so on and so forth. I hate it for them...but it's a fact.

Hugs,

Chyia, memory lane