A Kohen Who Lengthens His Prayer and Misses the Priestly Blessing

Is it permissible for a Kohen to extend his prayer even if it means he will miss the Priestly Blessing?

It is permitted.

The Kohen does not transgress a positive commandment when he does not begin moving his feet during the 'Retze' prayer, as explained in Siman 128, Se'if Katan 9 in the Mishnah Berurah. However, there is a loss of a mitzvah here, but since he is engaged in the mitzvah of prayer, he need not be concerned about the loss of the mitzvah. And even though prayer is a rabbinic mitzvah according to the Ramban, and the loss of the Priestly Blessing is a Torah mitzvah, nevertheless, he is not obligated to forgo it, as proven in Shulchan Aruch, Orach Chaim, Siman 72, Se'if 4, where it is explained that after burying the deceased and preparing to form a line for comforting mourners, if they can manage to say even one verse before the line, they should begin the verse, and if they cannot manage even one verse, they should not begin but stand in line. And the Rema there writes that this is only if there are hours in the day to read later. However, if there is no time later to read the Shema, he should read and not stand in line. And in Mishnah Berurah, Se'if Katan 13, the words of the Magen Avraham are brought, who wrote about the words of the Rema that since they have not yet begun comforting, it is forbidden to engage in comforting when the time will pass and cancel the reading of the Shema, but if they have begun comforting, they are exempt from the Shema even if the time passes. It is evident from the words of the Mishnah Berurah that although the rule of standing in line is not a Torah commandment, when he is engaged in it, he is exempt from the Torah obligation of reading the Shema.