I'm still looking at this, but Saul was a young man when he became king, too young to have adult sons.
You said: Attempted semantic apologetics don't solve the problems with the ages of Saul or Samuel.
The KJV renders the focal text in question at 1 Sam. 13:1 as ""Saul reigned one year; and when he had reigned two years over Israel, Saul chose him three thousand men of Israel... " So in this case, I need only switch translations.
But, indeed, this chronology remains problematic. If his youngest son, Ishboseth was 40 when Saul died, then Saul may have been 80 years of age at the time after 40 years of rule. But that also meant that he began to rule around age 40. that would explain how he could have a grown son, Jonathan, his eldest, at least age 20 or slightly more 2 years into his reign.
In the meantime, David was just a boy when he began to interact with Saul but was 30 years of age when he became king. If David was around 15 years of age when he killed Goliah, then Saul would have been 65 years of age and Jonathan as much as 45 years of age. Isoboseth would have been 25 years of age.
If Samuel were 60 years of age when Saul was appointed as king, then 25 years later he would have been 85. If Josephus is correct about him living another 18 years then he would have been 103 years of age at the time of his death.
This would mean that Saul was rejected as king after 25 years of rule.
But your focus on the issue of whether Saul ruled for 2 years would not apply to the KJV translation of 1 Sam. 13:1 since it does not assign this 2-year rule to Saul at all, but merely states that after two years is when he then appointed the army, at which time Jonathan was at least 20 as you stated. The fact that Saul was likely 40 years of age when he became king is also confirmed by a 40-year son at the time of his death, meaning his youngest son was born the same year he became king.
Thanks for drawing our attention to this issue.