Sorry for not answering your initial question. Airplane mode can interfere with the "Search" mode of the beacon. I have tested airplane mode, regular mode, played music, pushed data, as well as a few other scenarios to understand what affects a beacon. Each beacon I have tested has shown different affects at different times. My only conclusion is that the beacon really needs to be turned off when you begin your search.
I do agree with you for smaller slides that a single person doing a beacon search is the best method; however, for larger slides, multiple searchers can perform beacon searches together and will be very effective. As far as your other points, the person doing the beacon search should be the one with a probe and shovel. The other rescuers available should be doing an Immediate Search probing likely catchment areas and clues found in the debris. They should not be waiting for the person doing the beacon search to have a hit. Once a hit is made, yes they will get involved immediatly in the probing and digging.
Most of the research and training suggest that you should wait until you finish or exhaust your Immediate Search (including beacon search) before calling SAR unless you have enough resources. Remember, once you call SAR, you will be on the phone with them for a good 5-10 minutes giving them the information they need to get to you. Your window is really 15 mins for your partners best chance of recovery and SAR is usually 2 hours away unless you are close to a resort where patrol can respond. Even then, probably 30 minutes at a minimum.