G'day Scramjet
Number of problems with this one.
You can easily ascertain the required climb gradient (2.5% as has already been pointed out) and with some research you can find out your aircraft's advertised S/Eng Rate of Climb (Not always completely accurate for a number of GA Types I have flown!!).
Unfortunately, this is where the easy part ends.
You would then need access to the Procedure Designer to see if the Missed Approach Climb Path was obstacle limited and if so by what, at what distance and at what height. After a short course in Procedure Design, you could then make an informed decision regarding an amended minima for the single engine case. You would probably need to make two cases, one for each of Critical and Non-Critical engine failure.
As far as completing this process during preflight planning, good luck!!!
Given that your GA twin has no performance requirements imposed by CAO's upon it other than to be able to maintain a positive climb gradient at 5000' (ISA conditions) in the clean configuration, there may be more pressing questions worthy of your attention. You may, in fact, be trying to find answers to questions that have not been researched.
Should you find yourself in this situation with weather below landing minima, you would proceed to your planned alternate. Should you find yourself in the situation where there is unforecast weather below the landing minima (and yes, I understand that this can happen) then you are indeed in an emrgency situation and I would suggest you find the ground as best you can, as you suggested.
It's not a satisfactory answer but it's the best I came up with over a number of years doing it.
Cheers