I'm a driver at heart, so I'd take #3. The advantage is control of your schedule. Also, it would allow a visit to Hoover Dam or at least time to stop and admire the views from the new bridge across the Colorado River plus maybe a brief side trip out Route 66 segments. Helo flights give you an overview, but airspace rules keep them fairly high up these days. The coach is probably the lease expensive option,

Drive yourselves and spend a night at the SOUTH RIM. Do not fall for tours which take you to the West Rim; this is not part of the national park.

#3 for sure if you can spend an overnight at the Grand Canyon. Even if you can't stay overnight, #3 would still be my first choice. If you're just renting the cars for one day, pay the extra money and have at least one additional driver per car. It's a long drive there and back in one day but if you share driving duties it won't be so bad.

Rent 1 12 passenger van. http://www.airportvanrental.com/las-vegas-airport-van-rental.html
Make a reservation at the Hacienda casino/hotel which is quite close to Hoover Dam. There is a helicopter tour which takes off from a little hill next to the Hacienda parking lot. The ones who don't want to fly can take the van down to and across the dam. Park at the second lot (free) in Arizona and walk back over the dam into Nevada.
The next day drive in the van to the South Rim to see Grand Canyon NP.
If you can't get lodging in the park you can make it back to the Hacienda. Don't spend big bucks just to sleep in a hotel on the "Strip".

There are also fixed wing planes that do trips to GC. We took one in the 90's that went up lake Meade and landed at the airport near the rim, then took us on a bus to a place for lunch and to the Bright Angel, where we were able to get out for a short while then up to Hermit's rest for a stop and then back to Vegas before supper. It was fine, but since that time we've been back to stay over night many times. If you can do it on your own.

The driving time from Vegas to the GC is about 5 hours, but if nobody in the group is experienced with driving vans - I would consider renting maybe 3 cars - with 4 to a car.

If you are only going for a day - get up early and hit the road before Vegas traffic starts - ideally at Oh Dark Thirty - and you can grab coffee and rolls, whatever on the way and have lunch at one of the places on the Rim at the GC , such as Bright Angel Lodge - or the more upscale El Tovar.

Take the free bus shuttle (on off type) - toward the various overlooks (mainly to the west - you can more easily drive to the 2 or 3 lookouts to the east) and then head back to Vegas. Driving at night is no big deal if you leave the GC with a full tank of gas which should just about get you all the way back.

However - if you could spend a night at the GC it would be worth it - IMO.

A day/night in the GC would be far more rewarding(and less expensive, if you consider you won't be gambling) than the 1 night you take from Vegas. See the Sunrise and Sunset at the GC. Have a meal at El Tovar.

We were in Vegas last January. We did the helicopter tour because that is all we had time to do on our short trip. Although I had been warned about the West/South rim thing, again, we had to do a half day trip and that took us to the West Rim which is "not part of the national park" and all of that official-ness. Sometimes you just have to do what you can, and for us, it was either do the West Rim by helicopter or not do the trip at all, due to time constraints and other people travelling with us. We chose the former.

All I can tell you is it was one of the more memorable experiences I have had. Although I am sure others have had better, up close and personal experiences with the Canyon, I felt like I saw the GC and experienced its vastness and beauty in a way I will never forget. We did land for a few minutes and walk around, but the highlight was really just flying around and seeing that amazing terrain for all its wonder. (And seeing just how small we really were! I was surprised when I saw how small another chopper was in comparison to the canyon.) We did see the Hoover Dam. Although it was not directly in our flight pattern, we did see it briefly enough to see the dam itself and get a look at it.

The cost of the flight was about the price you listed, and they offered a package with a DVD recording of the experience, which I have never viewed again (and I am not even sure it was our exact flight pattern--just the voiceover of our group on a basic flight pattern of the package), so I don't recommend it especially if it's a price increase.

I think there were maybe 5 per helicopter, plus the pilot? Can't remember exactly. We booked through our hotel.

Bottom line: I am sure one of the other options is better, but considering you are trying to make 12 people happy, if it comes down to having to do a chopper ride in a half day over the West Rim, don't say no to the whole thing altogether. Do it.