I think that one of the problems that we are having here is understanding the meaning of the word "Paradise" We assume that Jesus was referring to heaven. The evildoer on the cross was a Jew and he would have grown up with the teachings of the Rabbinical schools in his mind.
While that man [and Jesus for that matter] was alive he would have been taught the meaning of "Paradise" and the writings that he would have had were: The Midrash [ Gen 68, Ex 48, Lev 405 etc] and the Babylonian Talmud [Berakoth 173, Shabbath 589] both of which began to be written some two centuries before Christ.
During the intertestamental period the vast body of literature mentioned above, [called collectively "Rabbinic Literature" and which included such writings as the Midrash, the Talmud, and the Targums] began a detailed description of the afterlife, including the meaning of Sheol. In time a concept developed which saw Sheol as being made up of two compartments or divisions. One was a section of abandonment called "Abbadhown" and the other was called "paradise" or "Abrahams Bosom" This section, which was a place of concious bliss, was the eventual reality to which pious Jews would aspire to on death. To this place the pious would be carried by a vanguard of angels. Much of the rabbinical literature alluded to above even went to great lengths to discuss how many angels it took to carry the righteous to "Paradise" or "Abrahams Bosom"
This rabbinic understanding of Sheol formed the basis of Christ's parable of Lu 16:19-31. So, rather than disabuse the Jews of His generation of a concious afterlife, Jesus used their own teaching and thus gave it a Divine Fiat. Thus when Jesus made reference to "Paradise" He knew what that evildoer would expect. That on that very day, both he, and Jesus would descend into the "Blessed" section of Sheol.
So, yes, on that very day, Jesus and the evildoer went to Paradise.
In Pauline writings, however we see a development of understanding which took place after Christ's resurrection. Thus, Paul uses the language of transition when He speaks of Christ taking the righteous out of the "Paradise" section of Hades/Sheol and bringing them into heaven. Thus it was only then, that heaven became the abode of Paradise. Whereas "paradise" in the gospels referred to the righteous section of Hades/Sheol, by the time Paul wrote 2Cor 12: 2-4, it was now placed in the "third heaven"
The only places where one would read of some concious place of a future Paradise earth, is in so-called "pagan" literature such as the Zoroastrian Zend Avesta. Which means that when the WTS affirm their belief in a future paradise earth, their basis is something other than Scripture.
Cheers