That's the build I use for an ultra mega turret. Slags and takes down everything, and the longbow means it lasts the entire duration without dying. I like to point a single point into Expertise and Healthy with the Legendary Soldier mod, just take out points somewhere else.
my build is similar to your 1st one. its been my favorite set up ive found.
mine is slightly different in that i have at least 1 pt in all tier 1 skills to take advantage of the legendary soldier mod
and i also use battlefront. the extra damage from axton while the turret is out is significant. love the double up longbow turret though. the thing wrecks just about everything and longbow makes sure a tough enemy doesnt just destroy it right away.
the long range placement (even without mag lock) is underrated i feel. its a nice advantage to be able to place a turret right in the middle of a mod or right behind their cover.
frees you up to do your thing since it draws aggro so well
this is my approximate build. IMO it offers a great turret and a powerful axton