You can farm the old chest loops, drop a bit of bounty xp on the greens, skip spending any glimmer on upgrading them, just max their xp and dismantle. A weapon does not need its upgrades completed to give max weapon parts. I've tested it. Same works for blues, but takes more xp so a bit more time. Otherwise, green weapon engrams are slightly cheaper than buying straight from the gunsmith. Hope this helps!