With 18, you'd need three cabs. Cab fare would be a teensy bit more, like $17-19 with tip.
The bus plus monorail approach would be not as fast as doing the same thing as before - walk to DHS and then bus to Poly.
My rule of thumb is to allow 30 minutes for each wait for a transportation option. It won't always be that long, but sometimes it will be. Sometimes it's longer. Then allow 30 minutes of travel time unless it's a super short trip. So that means 30 (wait) +30 (wait) +30 (combined travel) for the bus + monorail trip. The walk plus bus trip is 15 minutes (walking) + 30 minutes (waiting) + 30 minutes (travel), or 1 hour and 15 minutes.
Overall, I'd do the cab. How often are you going to do this kind of trip? Do it up right!

The cab to Poly is about 10 minutes and couldn't be simpler. Go to bell services and say you need three cabs to take 18 people to Poly. They do this all the time. Since you need at least two vans plus a sedan, you might allow an extra 5 minutes to get all of the cabs. You don't have to wait for them all to arrive. Designate three "cab captains" and give them the cab fare. Have them leave as soon as their cab gets there.
The bell services people will call the cabs over, tell the driver where to go, and help you into the cab. You might want to give the bell person a few bucks for the help.