I have found a way to accomplish what I was trying to accomplish, although it isn't by using function handles. In case anyone else is trying to do something similar, here is the method I used:
1) Get the output object instance name as soon as the constructor starts running by:
2) Use the output object instance name in setting the callback:
Since string based callback assignment executes in the base workspace, this directly simulates the equivalent command line action (and thus works).
Credit for the solution idea to Brad Stiritz: http://www.mathworks.com/matlabcentral/answers/16693-within-a-function-get-complete-command-line-calling-text-a-la-dbstack
If anyone can answer the question as asked (i.e. about function handles), I am still interested for future reference though. :)