As it is often the case, once one poses the question, one finds the answer.
For anyone interested in this, I give a quick summary now and try to write the full solution in the next few days.
Indeed my first ansatz was correct, but needed refinement:
So one first carries out the summation in...
I was trying to compute the equations of motion for the spin ##\omega_{\mu ab} ## connection from the Einstein-Palatini action
$$S := \int d^4 x e^\mu{}_ae^\nu{}_b R_{\mu \nu}{}^{ab}.$$
I managed to get the variation wrt. the connection to the form
$$ \varepsilon_{abcd}\varepsilon^{\mu \nu...