Fill up: to complete. Not the sufferings of Christ for our sins, but those things believers would suffer for the church and truth: The Church the Body of Christ. See also Romans 8:18 and 2 Timothy 3:12.
I have been over this line so much that I actually have the Greek word so translated in my failing memory! υστερηματα! Wow! An old Dawg can sometimes learn a new trick. (Just checked, I got it right! Accent on the ETA and there's a 'rough breathing' on the oopsie-daisy, I mean upsilon)
Do you have an analytical concordance? I think you will find that the KJV translators had an agenda when they chose that obscure clause to translate that word. Everywhere else it has a sense of deficiency. Here they, scandalized that Paul, of all people, could say that somehow there might be something lacking in the suffering of Christ, find some clunky phrase for their translation. But that is the plain meaning of the words.
Your take is certainly in the ball park, IMHO. (like I have a clue.) But we take VERY seriously indeed the Body metaphor for the Church. And so, since we hold the baptized to be incorporated into Christ, we hold that we share in His suffering.
Now, of course, in the most important sense, ΙΗΣ ain't messin' 'round when he says Τετελεσται. It is only by the 'perfecting' and complete sufficiency of His "work" that we are given the chance and the ability, by Grace (of course), to share in it.
I brought this up because I think it sheds light on the works v. grace/faith thing. Only a little light, but some is better than none.
In my deranged mind, it's kinda like the Trinity. God is One. But He does One His own way, so that somehow He is also Three.
So Jesus does "complete" but in His own way, so that there is still stuff for us to do. The completion includes some 'lack'.
To think about this stuff, as too many Catholics do, as hoops to jump through and tickets to get punched and so forth is to miss the whole point! Is it a horrible burden for you to study Scripture and expound it here and elsewhere? Do you do it hag-ridden, looking over your shoulder to see if God's okay with it?
I'd bet not. It's a blessing, a privilege, and a way other blessings come to you. You undertake it confident that where you fall short, God will forgive and amend you AND see to the amending (or, if it's REALLY a BIG goof, redeeming) of your work.
Am I at least part right? The work does not earn grace (that amounts to a contradiction in terms, as though one could 'deserve' mercy), but grace comes through it nonetheless.
It is not a burden to me to go to Mass, to pray my office (breviary, whatever) and Rosary, and to go to confession. I do not approach these things as 'tit-for-tat' matters. Sure, there is sometimes a reluctance, a kind of holding back, but, IMHO, that is just the enemy trying to keep me from doing something that will bring me pleasure and 'health.'
I remember one evening Mass, just before Mass began, a friend walked out of the confessional and up to where she usually sits. She had a nice, happy, calm, smile on her face. And I thought,"Now THAT's the way to come to worship! Assured of grace and forgiveness and happy with it. This is someone ready to 'do' the Eucharist -- thanksgiving with all her heart.
So the seeming "burden" of works as vehicles of grace is, to me, looking at it entirely the wrong way. Any Catholic, any person whatsoever, who thinks he can come to God and bring a portfolio and resume to bargain His way out of Purgatory and into Heaven has it all wrong.
When I see God, I mean to THANK Him for all the wonderful things He let me, enabled me, helped me do. I mean this most seriously. Glory to Him for sometimes letting me not mess up too badly!
Oh, in that connection, (wha'?) I want to say that I see Purgatory not as a burden but as a mercy. I mean YEAH, I wouldn't mind being martyred so I can skip that step. But just as, when dirty, I want to be washed so, I take great hope in knowing that here and hereafter God will "put away all my sins," and not only the sins themselves but the scars and weaknesses they have left in me.