It also seems that because of his high workload and letting the aircraft get ahead of him (note the speed mentioned at 1.6 DME in the report!) he gave himself a lot less time than he otherwise would have to consider his options.
Standard procedure surely is to go back to the frequency you came from if no reply on new frequency
Well quite; yet to have this happen on final approach but several times enroute I've had to go back to the previous, either because I've heard it wrong or been given it wrong. As the report mentions though the fact that the radio on this aircraft had failed before may have lead him to assume in the confusion of the moment that it had done so again...
As for changing to 7600 I agree it is a bit fiddly on the G1000.