Capacitance node calculation
I`ll try to answer my own question with Vicents suggestion. Applying wye-delta transformation gets an analyzable circuit:

Ca = Coposite/(C1*C2 + C1*C3 + C2*C3)
Or since C1 = C2 = C3 = Cd (delta):
Cy = Cdelta*3

Further simplifications
Cg = C4 = C5 = C6
leads to 
Ctotal = Cg + 1/(1/Cy + 1/(2/(1/Cg + 1/Cy)))


Which coincidentally gives exactly the result with my values as my naive approach of pretending the original C3 didnt exist. 

Hopefully somebody in the comments will correct me if the inductors will skew my results either way.