1. agree with the duty-free-on-arrivals idea : it's a sort of extension of the process in the States where your duty free is bagged and tagged, and then delivered to you on the jetway before you board; it would just be a small step to put all the bags in a container and deliver them to pax on the jetway after they land.

2. why not introduce explicit size limits for the second bag, based on the space under the seat in front (OK, except for bulkhead seats etc)? I still have my old Globetrotter from about 1980 which used to have a label "approved by British Airways for under-seat stowage" or something. The size would I think be something like the limits that were in force when hand luggage was first reintroduced after the ban in 2007(?): the area of a large laptop and about six inches deep.