Hi, I'll tell you a few thoughts about it. Actually I just wrote something longer, but then the whole thing was erased when I tried to upload a file.
Triplet carbenes are rather sp hybridized and therefore linear.
The bonding angle in sp2 carbenes decreases with higher EN difference. That is explained through VSEPR rules.
Triplet carbenes are in general more stable because of spin coupling energy (cf. high spin complexes).
It seems that with increasing EN difference the singlet carbene is more stable (also in Dichloro-carbene). That probably comes from the fact that the sp2 orbital can bond better to a highly electronegative atom. In an sp2 orbital the highest electron density is farther away from the nucleus.
I added an image that shows the energy levels of the different species. But it does not show as much as I thought it would. you find it here:
http://stud4.tuwien.ac.at/~e0425252/Carbenes.skcHybridisation in higher elements normally looks different because d-orbitals are also used.
hope that helps a little bit