@Ten Centuries - Perfect!!!
Thanks for the sqlcmd bit - that did the trick for me.
My current configuration is both SQL and DAC running on non-standard ports (say 41433 and 41434 respectively), browser service is disabled and Hide Instance is enabled (all of these from CIS Benchmark recommendations)
I was running into a brickwall being able to connecto to the DAC through Management Studio - using sqlcmd from the command line did the trick. Noting that you did not include the -A to have sqlcmd connect over the DAC I tested stripping out "ADMIN:" from the Management Studio connection and that seems to be working perfectly.
I connected to: <servername>,41434 - that worked perfectly.
Next I verified I was using the DAC by attempting to make another connection over 41434 and ran into DAC in use error.