as for possible clutch dimensions/solutions:
as I said, AFAIK 115 mm diameter (friction plate OD not clutch OD) is the smallest "of the shelf" clutch you can buy.
IIRC the Honda F1 clutch had 97 mm friction plate OD, but there where smaller ones made for others.
Keep in mind, that some engines (e.g. Porsche) are sensitive to axial loadings on the crankshaft, and the manufacturers define max. release load on the clutch.
All F1 clutches (today) are pull type clutches.
But all in all the clutch will not be one of your biggest problems.
Here some more detailed informations on the dimensions of a commercial available 115/3 push type carbon/carbon clutch.
http://www.apracing.com/drawings/cp8153cd.pdf