Unluky? Probably yes, but not to much
Setup is wrong? Yes, Botd BA is a mediocre choice, LW is a terrible choice, 2 Grief PB is going to give you more than double damage (more damage more faster runs)
Kill fast? Not really, Barb is kinda slow, and with your weapons choice even mooore slow.
Any advices? tele in switch with 2 hoto, change weapons to double Grief PB, change magefist to Laying of Hand, change amu with HL, Rare ring need 10fcr and life and mana leech, change nagel for a 40mf magic ring and I would change Shako for a Ist Guillaume face.
105fcr on switch (faster tele), tons more of killing speed, more than enough mf.
Is Light sorc better? yes, a lot better, but is not to good for travi temples, you should skip this with light sorc and add full chaos run for example to the route.
Use this:
Lightning
Griffon Eye with Facet
Mara
Hoto
Enigma
Spirit monarch 32+fcr
Chance guards
Arach
2 soj
war travelers
CTA/Spirit switch and some MF/FR charms to cap fire res, then Gheed and some more MF small charms (about 250-300mf is more than enough with this killing speed, add some skillers)
Max Lightning, Chain Lightning, Lightning mastery, Charged bolt
1 point into Warmth, static field, Teleport (optional if you use only enigma) and Frozen armor (optional), rest into Nova
Act2 Nightmare ofensive merc (might aura)
Andariel visage with 15ias(+fire res) jewel
treachery
eth infinity in threser or Giant threser
Defensive mercenary works too, fortitude instead of treachery is also an option
Str for gear and rest vita.