I like your understanding and agree.
It’s possible that Jesus had been reciting Psalm 22, which concludes with “He has done this.” In the Greek it comes out “tetelestai” or “It is finished.” But the “He has done this” refers to the events prophesied late in Psalm 22.
His death on the cross was complete and finished. What He was about to do on the “other side” was yet to come. When that was done, He was raised. These upcoming events included meeting the repentant thief in paradise and some kind of preaching to those in the realm of the dead, Sheol. I’ve seen an attempt to diagram this, but in some places the scripture still seems vague.
In redneckese, Jesus’ words might be taken at that point as “He’ll git-r-done.”