Fundamentally, you want the design to have outlines which describe a single set of closed regions.
So the crossbars of the As:
should be unioned:
and there the 4 crosses itself:
has to be corrected:
For the egg, it will need to be inset so that the regions which are in contact with its perimeter may be resolved:
For the small hearts at the bottom it will be necessary to duplicate and offset them to the outside:
and then punch them out of the larger shapes which they overlap:
The same will need to be done for the small hearts at the top:
For the interlocking hearts, that requires Carbide Create Pro:
so we will instead just move one to the fore and remove the balance:
Eventually one arrives at:
h
which may be joined into a composite path:
which should then cut as expected:
Attached as a v8 file.
House of Angela Sign_v8.c2d (1.1 MB)