Recently, modder Wombat returned to Fallout: New Vegas and introduced a set of reworked character movement animations:
The set includes all basic "standing" movement animations: idle, walking, running, jumping, and landing, each with directional variants. Additional animations for melee attacks and minigun fire have also been added.
In third-person view, the character no longer contorts when using the minigun:
The "Enhanced Animations - 3rd Person Movement" mod for Fallout: New Vegas is available for free on Nexus Mods.