I have the Sig Sauer ASP Supertarget which is mechanically the same as the 6004. I did take the barrel out and relive the breech on my lathe, but the other thing I have found that helps is to hold the top 'slide' in my left hand with the breech pointing up, then use my right hand to load the pellet. (I am right handed).
With all the other SSP's I have had, I used to keep my right hand on the grip and load with my left hand, meaning the breech was point away from me at twice the length of the pistol. For pellets with very stiff skirts, I made a brass pellet seating tool; lead-free pellets are so hard the pistol hasn't got enough power to move them!

Hope this makes sense and helps...