Aside from being really good at killing, you can try a variation of the Battle Medic loadout I posted earlier. If you don't have enough loadout points, use FAT 2 and/or Reviver 2, and drop the Shotgun for maybe the Semi-Auto.
Or you can replace Reviver for Crafter 2 or 3 instead (always 3 if you have it unlocked). Gifting items is easy. You don't have to engage. Just go for the supply boxes, and stick with your team.
It's really easy to get a lot of parts with any of those skills without having to get a lot of downs.
Doesn't matter which gun you use.
And don't forget to mark. You get parts for that as well, and even if one mark doesn't get you a lot, it adds up. It helps your teammates, too.
Survivors is actually a great mode to get a s*** ton of parts. Just survive as long as you can, and if your teammates are cool with it, try to extend the match for the entire 7 rounds.