My father died May 11th, 2020 (the 17th of Iyar, I believe) and were coming up on the end of the 11-month Kaddish period. However, I am not totally sure when to count as the end of Kaddish. I have been assuming that it is April 12th or 19th, but I am not completely sure.

The end of the kaddish period, according to the Mishnah Berura, corresponds to eleven months from the day that the 'niftar' (deceased person) was buried. However, in the event that many days lapsed between the death and burial, then the last day of kaddish would be eleven months from day that the person died. If your father was buried on May 11th-- the 17th of Iyar-- then the kaddish ends on the 16th of Nissan (Monday, first day of Chol Hamoed). If he was buried on the 18th of Iyar, then the end of the kaddish is the 17th of Nissan; meaning Tuesday, the second day of Chol Hamoed) The yahrzeit, an annual occasion, always corresponds to the day that the person died, not to the day of the burial. (see Beur Halachah: 132) . May you only experience much happiness!