Got this achievement yesterday using this method and took less than 15 minutes!
Have someone host a Full Boat session on TA, and when the time comes for the session, start no matter how many players you have on TA(we had 3 in the session on TA). Have the host start the match, and everyone join his session, also invite anyone you know that might want to do this. We had 8 people in our lobby when we were ready to go.
THEN! Have the host send everyone a message just in case he's not in their friends list(very important, otherwise you'll have to type in names manually), and everyone except for the host agrees to scatter for 5 minutes.
For 5 minutes, everyone start joining and leaving every Homefront match you can find as quick as you can, until your recent players list is full.
At the end of 5 minutes, all the original players rejoin the Host, and then send an invite to ALL your recent players. That should result in anywhere from 40-250 players being invited.
I recommend a voice message unless you're really good at typing.. something like this: "Hi! We're doing a match for the 16 player achievement in Homefront, just a few slots left, if you want the achievement join quick please!" That worked for me :-)
You should have no trouble filling the match up if everyone did the match hopping, just wait for it.
Make sure everyone is "In Lobby" so the host can start the match, and make it GROUND CONTROL. We had 15 players unlock it first try, just one player needed a rematch to get it again, so most of us quit out and replayed. Also, expect players to go wild and start shooting enemies and each other when the match starts. Don't worry about that. Just use invites if you need a redo.
Thanks to SupernaturalH2O for the ground control idea!