In my case I choosed Parker over his masteries. You can choose O'Brian as well. Any characters which have handgun and shotgun masteries are welcomed. IMPORTANT: decrease your character level before to start the stage! -10lvl (so it will be lvl 21)
Weapons and custom parts... Hmmm, here's the most interesting... The thing is this method requires Dictator or Parker's Government. Not an option to try to farm it spending a lot of time but an option to buy DLC (this isn't an ad LOL). M40A1 with 4-5 slots : you definitely can find it ("Steady Hand" tag will be superuseful). Windham with 4-5 slots- the same as with M40A1, it's not super rare weapon. Do not forget about RENET events and rewards :)
Custom parts. Well, the worst news is this method requires 3 Medals of Courage and 3 Full Bursts (!!!) for every weapon. You also will require Long Magazines, Narrow, Dehumanizers, Giant Rabbit Foot (as an options), Daze etc. You can check out the build at the end of the video

Conclusion
Pluses:
+ fast farming BP and EXP, very effective but it requires Trinity Bonus.
+ doesn't require a very expensive customization
+ doesn't require Gluttonies and Autoloaders
+ doesn't require a lot of unique weapons

Minuses:
- Dictator... The method is built on it
- 3 Medal of Courage + 3 Full Burst (seriously?!)

P.S. Thanks to Armhellion for the shared knowledge