Was the mistake in Gilgal severe enough to cost Shaul the monarchy?

Shmuel concludes Saul's punishment and they travel to the battlefield.

Shaul errs and offers karbanos prior to Shmuel's arrival

Many jews go into hiding, while the army that is with Shaul panics and starts to disperse.

After Yonasan assasinates the Pelishiti Commissioner Shaul gathers Klal Yisroel for battle.

Shmuel concludes his speech by reassuring and further instructing Klal Yisroel

Hashem causes a miracle of rain and thunder; the People beg Shmuel to daven on their behalf

Shmuel continues his rebuke and describes a miracle that will happen to show Hashem displeasure.

We cover 3 issues with the pasuk: 1. What are the nicknames used? 2. Why does Shmuel speak in 3rd Person? 3. Why does Shmuel pick these 4 Shoftim out of a much longer list of names?

Shmuel recalls how each time Klal Yisroel sinned and repented Hashem sent a Shofet to rescue them