In the mailing list we came up with the following ideas (more ideas are welcome!):
Part of the solution would probably be to encourage collaboration in PhD projects ("more hands on deck").
Problem: PhD requirements often are not set up to foster collaboration among PhD students because they enforce first authorships.
A possible solution: The Study Swap model where two or more labs agree to collect data for the other lab and vice versa.
This model can work quite well for many studies, where, for example, some additional questionnaire from the other lab can be added to the end of your own experiment. Of course the model does not work for all kinds studies (e.g. very specialized lab studies).