Proving the WTS appointment in 1919 from the Bible requires some incredibly convoluted scriptural gymnastics. In addition to the points noted above, Malachi 3:1-5 comes into play. In this cryptic passage, God promises to send "his messenger" to cleanse his temple with the lye of a refiner. The WT interprets thiese verses as having two fulfillments (of course).
First (if I recall correctly), this was fulfilled when Jesus came down to earth. He judged the nation of Israel as being unclean and started his own religion--Christianity. The second fulfillment was in 1918-19, when Jesus came back, judged all the religions claiming to be Christian, and selected the WTS as his organization.
So this is how they get the parallel between Jesus' earthly ministry and his 1918-19 judgment. In the first fulfillment, it took Jesus 3.5 years from when he was anointed until he established the new Christian congregation (Pentecost 33 A.D., I think). Thus, as a holdover from Russell's parallel dispensations, the WTS assumed that Jesus would take 3.5 years from being installed as king until he started judging the other religions and picking the one he liked.
Note that I'm doing all of this from memory, so I may have gotten some details wrong. If so, feel free to point them out. But I think my comments above accurately reflect current WT teaching on the matter--at least at a high level.
Also, you asked about whether it would be wise to mention that modern Bible Student groups adhere more closely to what the WTS taught in 1918-19. I don't think it would add much to the conversation to bring this up. The JW response is that the light gets brighter and those Bible Students are stuck in the past. It would be a distraction and would likely lead off on a tangent.