Fabian,
I do not know of a way to do this with the built in commands, However, you can easily write your own.
You can get the labels with this command:
labels = Cases[model , Rule[SystemsModelLabels, lst_] -> lst][[1]]
From this you can create your own mySystemsModelExtract that finds the labels in the list of labels above (by Position) and feeds that to the SystemsModelExtract function. You need to decide on a syntax for your command but it should work well.
Regards,
Neil