Is there complex Gross - Zagier in this case? Their work also excludes this case. If there is, one can expect the p-adic Height of therse Heegner points to appear in p-adic version,  as in the case of Perrin - Riou. There is a paer of Conrad on complex Gross - Zagier which includes this case. However, I do not know whether one can deduce complex version from that paper.