I now have a definite timeline for the life of Paris (aka Alexander), prince of Troy: born 1231, died 1184 aged 46/47. I'll publish the full timeline separately, but wanted to bring up that I've been looking into his parents and siblings, trying to give each of them a few dates here and there.
Priam had many children. Relying on Homer, Apollodorus, Hyginus and Virgil, I've been able to identify 84 children: 16 daughters and 68 sons. I'll have to check again, as I might have missed a couple. He had two wives (Arisbe and Hecabe), and a number of "palace women" (i.e. concubines). By Arisbe, he had at least one son, and soon enough divorced her to marry Hecabe (or Hecuba), the well known queen of Troy. Hector was their first born and Troilus was the last born son. He was still a young teenager when he was ambushed and killed by Achilles (an event that I date to 1191, quite early in the Second Trojan War). As a result, I place his birth in 1205. Apollodorus tells us Paris was their second born. Hyginus says Paris was born much later, but I choose to reject the latter claim, as I consider Apollodorus more authoritative and it agrees better with my timeline.
Indeed, if Paris is the second born, I would place Hector's birth to 1233, which means Hecabe has been birthing children for at least 28 years (!!). If Paris is one of the later children, that birthing period is much longer. If Hecabe gave birth to her first child in her late teens, she would have given birth to Troilus in her mid-forties, which works nicely.
I have therefore set Hecabe's birth to 1251, which makes her 66/67 at the fall of Troy. Priam's birth is more tricky, because he was a boy when the First Trojan War occured, which I have not dated yet (it ties in with the timeline of Heracles and either his capturing of the girdle of the Amazons or his participation in the expedition of the Argo), but I expect Priam to be born around 1270/1265.
Now "all" I have to do is date Paris's brothers and sisters, and given their number, it'll be a labor of its own.