Our SOP is to continue the approach and land if the ASA continues to show Land2 or Land 3 (757 & 767). Bearing in mind the reliability of Autoland systems (CAT II and III ground equipment included) I have always felt this a more sensible option than diverting single crew. Once saw someone "divert" in the sim for an incapacitation and the workload went through the roof with reconfiguring, climbing to diversion Flight Level, change of ATC freqs, reprogramming FMC, fishing for charts, setting up nav aids etc etc.
I would find the prospect of a "single crew" VOR or NDB approach to minima far more daunting than pressing App and watching it all happen for me.