Jehovah's Witnesses believe1 that 144 000 of their number are
different to the rest in that they will go to heaven, whereas the rest
(presumably several million) will live on paradise Earth.
I'm wondering how near to complete they believe that they are now, eg
25%, 50%, 99%? And do they keep records on the 144 000 so that they
can answer this exactly?
The easy answer, devoid of speculative and distracting outlines:
No, they have no idea on percentages, and often revise their understandings on this and related things.
Its important to remember the roots of JWs. The main intent is to restore pure worship, and labor greatly to unravel scriptural mysteries.
The 144,000 number comes directly after the 666 number, showing a contrast. 666 is associated with a name, 144,000 is associated with a name.
A name in the scriptures is tied with a person's activities / reputation. (Ecclesiastes 7:1, Revelation 3:1, Revelation 14:1)
By the fact that 666 (or 616?) is openly acknowledged to be a calculable mystery, it would not be surprising if the same were true of 144,000 in comparison, both being numerical results of related allegorical puzzles found in the scriptures.
The identities associated with the 144,000, and knowing it's completeness, is not something entrusted to men, but God:
Every way of a man is right in his own eyes, but the Lord weighs and
tries the hearts. (Amplified Bible)
Compare this to the parable of the faithful steward and the wise/foolish virgins, as well as the related slaves/talents parables. There is a lot going on here numerically. JW's have at least been smart enough to see relationships here. I wonder who will be entrusted to know the final summation of it all? ( Genesis 41:15-16, compare Matthew 7:8 )