I can offer some opinions based on my own experience.
1) For strength and conductivity, 5356 filler is correct for 6061-t6.
2) Helium is generally added for thicker sections of aluminum.
3) Using a push system for aluminum wire is a tough way to go and will often cause a lot of headaches with "birdnesting" as you described. I know of no filler metal that in itself will solve this problem. A teflon liner may help.
4) A dirty weld area can be caused by A) dirty work piece, improper or inadequate cleaning prior to welding. B) inadequate shielding gas. C) inproper electode angle or improper direction of travel.
Mike Sherman
Shermans Welding
This question asked raises numerous questions, best long term answer for yourself and your company is to attend AlcoTech's welding school in Traverse City, MI It is only three to four days.
Short Term Answer: Mount your drive rolls or feeder 4Ft away from the torch, don't know the robot name, but they all have methods for this.
If you are not anodizing after welding consider 4047 filler, you can get an almost "smut free" weld, have someone wipe the parts immediately after welding with a cotton cloth, the smut will come off easily. Use 100% Argon on thin sections with any filler for 6061.
Tune the drive system, drive roll pressure, alignment, liner, contact tip for aluminum wire, etc.
Regards, Brad