You have ask the age old question , my bias is for a day hike , cuts the weight carried down to a few pound and since you are not geared up for overnight , first time overnight trip would open the door for gear choice problems , how much and what is needed , you can rent most of the gear but again what do you need and are willing to carry that weight. I think in terms of energy output over the distance .
Overnight hike again I differ from many : 3 days . Hike to Outpost first day summit the second day return to outpost and spend the night exit on day 3 . This cuts the carryweight down to about 7 miles vs 12 miles to trailcamp also allows for extra day to adjust to the elevation , carry a very light day pack to the summit . Trail camp can be windy colder and crowded. Trailcamp elevation is 12,000' so about the area many will not enjoy a restful night.
Day hike as you suggested arrive a few days early , Stop in Mammoth and if the gondoal is operating ride to the top spend some hours , Bristlecone Pine area out of Big Pine another area to get some elevation 10,000 -11,000 and see the amazing trees , spend the days high and sleep down in the valley . Horseshoe meadow drive to 10,000' short hike around . Focus on hydration and electrolytes and snacks , I don't suggest doing long hikes a few days before a Whitney hike. On the day you plan the hike think about a pace of about 1 mile per hour I know that sounds way slow but it allows an easy pace that you can maintain all day ( call the guides pace) You can increase the pace coming down but focus on the group and see how every one is doing. The hike can be 14-18 hours so going slow up gives you some reserve enery to come down.
You mentioned your group hikes are in the range that adding a few miles on training hikes should get the group ready for the distance , foucs on some long hill climbs and long down hill hikes , down hill can put pressure on your feet and lower body . Poles will offset some of the down hill pressure.
Hey last hint try to pick a full moon period , keeps you out of the sun exposure (heat) cool period before sun rise and watch the sunrise around trailcrest !
Which every you choose Whitney is a great hike for so many reasons .