In my personal capacity I have built MongoDB from source and published binaries on Github here. While I have not attempted to run the binaries on a Pi 3, you can give it a try and report back.
The Illegal instruction error you are hitting is well documented here and on StackOverflow. Search for the many threads of people hitting the same issue (I have included a random sampling).
The storage engine of MongoDB, WiredTiger, is driving the requirement for a microarchitecture that exceeds that of Raspberry Pi’s and this is not going to change anytime soon.
Feel free to raise an issue on the Github repo if there is an issue with the binaries or procedure to run them.