Another possible solution: if the mode change is not unanimous, ask the pilots!
The pilots might not know, (e.g. when landing in fog - famous accidents happened because of this), but at that point a go round or diversion to another airport seems to be the safest plan of action.
The pilot in command has ~no spare capacity during touchdown, full focus is required for rudder and stick. Especially during crosswind landings. The other pilot probably shouldn't be expected to make such a decision in a second out of the blue.
The copilot could press a button as soon as the plane lands, if and only if he is certain the plane touched down. Then, if the computers can't decide, use that input for a decision. Literally asking and then awaiting a reply is slow indeed.
