I don't see the cause for agitation. Some narrators are obviously unreliable, and Kirk in "The Deadly Years" is definitely that. If he said the sky was blue, there would be good reason to distrust him (and the sky in fact was
orange, potentially a crucial fact in diagnosing and curing the afflicted heroes

).
Nothing wrong with Kirk being 34 - I never indicated there'd be a problem there, other than the utter unreliability of the source. But narrators in the 2009 movie would appear unafflicted, so their 2233 for the year of birth should be trusted. If "The Deadly Years" needs to take place in some year other than 2267, then Kirk's age there needs modifying, and the opening for that exists.
Didn't Riker once comment that he wanted to beat Kirk's "youngest captain" record?
No.
We know Tryla Scott is the 24th century gold standard there, but her age in the episode is unknown and so is the age at which she achieved the rank/position. Or perhaps she graduated older than Kirk but also joined Starfleet at a later age and therefore wins the race?
Nor do we know whose record she broke there, although the other three in that cave were apparently contestants (Picard probably excluded), or by how much. Perhaps Kirk had never been a serious opponent?
The age at which Kirk achieved Captain is equally unknown (unless we decide it was between his pilot episode and "Corbomite Maneuver", as his sleeve braid changes there, but some don't want to interpret the pilot braid that way). And perhaps Tracey or Decker got the promotion even earlier on?
Apart from these musings, the concept of "youngest at X" is never mentioned in Trek! Except in "Rascals" where Troi jokes that the rejuvenated Picard could now become the youngest Admiral ever.
Timo Saloniemi