You didn't mention cars, so I assume you plan to do this via public transportation. If I'm mistaken, please say so at once so folks with driving experience in that area can help you.
I will be in that area just before you are. I can't tell you what you should do, but perhaps this logistical information will be helpful. With 11 people, you may have really serious problems finding a place (or two) to stay, so I recommend looking at lodging availability before you get too mired in other aspects of your planning. It may well be that you can only find the space you need in one place, which would at least simplify your decision-making.
Fast boat Bergen to Balestrand (3 hr 55 min or 4 hr) and Flam (5 hr 40 min or 5 hr 25 min).
Departures Sun-Fri at 8 AM and 4:30 PM, Sat at 8 AM and 2:15 PM. Second departures don't go all the way to Flam, terminating at Sogndal.
I don't recommend this between Bergen and Balestrand; reports are that most of the trip is through wide-open water so not especially scenic. This is your fastest option between Balestrand and Flam (1 hr 20 min to 1 hr 45 min); buses take longer and require a connection. https://www.norled.no/globalassets/hurtigbat-priser-og-ruter/2022bergen---sogn---flam---bergen2.pdf
Note that there's just one boat a day between Flam and Balestrand in each direction.
Train Bergen to Voss (1 hr 6 min to 1 hr 20 min), Myrdal (1 hr 48 min to 2 hr 24 min) and on to Oslo.
On the random weekday I searched (Wed, June 22) there were departures at 5:30 (Voss only), 6:19, 6:55 (Voss only) 7:21, 8:15, 8:29, 9:28, 10:36, 11:30 plus seven more trains departing in the afternoon and evening.
Look up schedules here: https://www.vy.no/en
Voss and Myrdal are not that far apart. I'd think (without looking at detailed schedules) you could go from Bergen to Myrdal and do the fjord loop in the same direction as people traveling from Oslo, taking the Flamsbana downhill, meaning you'd travel Bergen-(passing thru Voss)-Myrdal-Flam-Gudvangen-Voss-Oslo. (I have no idea whether that makes a difference in the scenery.) You'd cover the Voss-Myrdal section twice. VY.no will sell you a through-ticket to Flam if you search for Bergen-to-Flam ticket; having that Flamsbana ticket ahead of time could be critical. Departures with that connection are listed at 6:19 (sold out on June 22), 8:15, 8:29, 9:28, 11:30. However, I see that there are some very, very tight connections in Myrdal when you travel in this direction.
For the standard trip Bergen-Voss-Gudvangen-Flam-Oslo, you'd be starting your final leg in Flam. VY.no will sell you a ticket from Flam to Oslo (5 hr 47 min to 7 hr 35 min), including the Flamsbana. Departures (June 22) are at 9:00 AM, 10:15 AM, 2:10 PM, 4:40 PM, 5:50 PM and 7:25 PM.
Passenger ferries Gudvangen-to-Flam take 2 hours. The Fjord1 boats run only twice a day, departing from Gudvangen at 12:00 and 5:50 PM and from Flam at 9:30 AM and 3:20 PM. The older boats (quite possibly cheaper) are operated by Lustrabatane. Its boats depart from both Gudvangen and Flam at 9:00 AM, 1:45 PM and 4 PM.
NorwaysBest sells tickets on the Fjord1 boats: https://www.norwaysbest.com/things-to-do/fjords/fjord-cruise-naeroyfjord/
Lustrabatane: https://www.lustrabaatane.no/flmgudvangen (Right-click and choose "Translate to English".)
Should you need it, there is bus service between Gudvangen and Flam. The trip takes 20 minutes. Buses depart from Gudvangen at 12:00, 1:30, 5:30 and 6:30 PM and from Flam at 11 AM, 1 PM, 5 PM and 6 PM.