Turin=Achilles?

[Tuor in Gondolin]

In reading the Iliad (well, okay, listening to a cd lecture by Elizabeth
Vandiver) I noticed an increasingly interesting parallel between
Achilles and Turin. Given Tolkien's schooling in Greek language and
history, I wonder how much was conscious and are there other classical
parallels mto Middle-earth personages (I tend to view the valar as more
archangels then Greek/Roman gods, but still...).
Granted, Tolkien says the chief inspiration was the Kullervo, there
seem to be interesting Achilles similarities.

Consider Achilles/Turin:
1) He's the greatest warrior in archaic Greek mythology
2) They both have tempers and make rash decisions and then
stubbornly hold to them- Turin won't go back to Menegroth and
Achilles won't rejoin battle even though Agamemnon handsomely
apologizes for swiping Achilles concubine
3) Both die young, fighting as warriors and achieve great things
for their sides---Achilles kills Hector, Turin kills Glaurung
4) They both have cranky superiors who tick them off
(Agamemnon and Thingol)
5) Both have a hand in their best friend's deaths (Achilles by
letting Petroclos use his armor)
6) Both unjustly kill people due to their rash temper
(Achilles the young son of Priam-Lykaon, and Turin Brandir).
The commentary by professor Vandiver on Achilles could be easily
transposed to Turin:

He kills entirely without pity. He kills even when he should
not. Even when he ought to show mercy. He kills inappropriately.

7) Both Achilles and Turin's fate are largely predetermined, unless they,
in effect for their milieus (sp.?) choosing cowardice, eschew prowess in
battle: Achilles by choosing a quiet life without lasting fame and Turin by
abandoning his (granted frequently misguided) defending those he
holds dear, his family and former home and Finduilas and Menegroth.

Btw, both Agamemnon and Thingol seek to repair their relationships
with their prickly warriors and their overtures are both rebuffed.

What do you think? Any other possible Middle-earth classical parallels?