Overtime Rules Contradiction

A very intelligent friend of mine pointed out a potential conflict of the overtime rules and I’m curious if anyone knows how this conflict would be resolved.

Rule 16, Section 1, Article 3, Subsection A states that “both teams must have the ability to possess the ball once during the extra period.” Also Subsection C of the same rule states that “if the team that possesses the ball first scores a field goal on its initial possession, the other team shall have the opportunity to possess the ball.” HOWEVER, Subsection D states that “there shall be a maximum of one ten minute period, EVEN IF the second team has NOT had an opportunity to possess the ball.” (emphasis mine)

Let’s say the Chiefs and the Eagles go to overtime. The Chiefs win the toss and elect to receive. The Eagles kick off and the Chiefs get the ball on the 1. Their drive eats up almost every second of the overtime period, and they kick a FG as the clock hits zeroes.

Subsection A and Subsection C both suggest that the Eagles would get a chance to possess the ball, but Subsection D suggests that no additional time would be added to the clock. So what happens? Do the Eagles get an untimed down to go for a Hail Mary? It seems like that is the only solution that would satisfy all three requirements of the rules.

I would LOVE it if anyone who knows the answer for a fact would weigh in on this discussion. Thanks in advance!