I've been doing melee statistical tests with luck stacking. I've got a prilimary report here. This is

still not statistically sound since I haven't really done enough rolls, but here's what I've found so

far

This IS stackable to +10 luck
2 Tymora's bands
HoF ONLY version of Lucky Knucky
Bard Song
Luck Spell

I have yet to test any items "Of Luck" that instead of adding to general luck, add to saving throw luck.

Here's my test setup:
Attacker:
Lvl 1 Rogue, 10 str, 10 dex, BAB=0, Hasted, 2 attacks/round
Mass Haste
Staff

Sandbag:
LvL 30 Barbarian
600 Life, 7 Dmg Resistance
14 AC, 10 base, 4 Mass Haste

Preliminary data (16 Attacks Recorded)
Attack Rolls - Crit Roll - Dmg (Includes Dmg Resistance)
20 - 20 - 05 (12-7)
20 - 18 - 05
20 - 20 - 05
17 - NA - Im (all 6 dmg resisted)
20 - 20 - 05
11 - Miss
20 - 14 - 05
20 - 14 - 05
14 - NA - Im
20 - 14 - 05
16 - NA - Im
20 - 20 - 05
16 - NA - Im
20 - 20 - 05
20 - 20 - 05
20 - 20 - 05

Summary:
All the damage rolls rolled for a 6, which was expected with 10 luck.

The lowest roll seen was an 11, which matches 10 luck. I could just be lucky, so it might go lower. Especially with only 16 attack samples.

20's are showing up alot, which seems to suggest, to roll a 20, a "natural" roll of 10-20 is needed, meaning a guaranteed 50% critical AND hit even on an enemy with infinite armor! This is not the case of rolling 11-20, with each roll having a 1/10 chance. This means instead 20 has a 1/2 chance, with the remaining probabilities 1/10 each for lucked rolls of 11-19.