If it wasn't just dumb luck for the JFK plotters, then I would research the persons who actually got the job for LHO -- not Ruth Paine, but Bill Randle and Linnie Mae Randle -- the sister of Wesley Buell Frazier.
It was LInnie Mae who told that group of women at the home of Dorothy Roberts, with whom Ruth and Marina were having coffee, that there was a job opening at the TSBD.
Because of that fact, Marina nagged and nagged Ruth until Ruth called the TSBD to sell LHO as a loyal ex-Marine whose wife was pregnant again, and really needed the job.
Yet Linnie Mae Randle and Dorothy Roberts had known for a solid month that the woman staying with Ruth Paine was a Russian who couldn't speak English, and that her husband had no job (which was why Ruth was taking care of her).
So, that means that Dorothy and LInnie Mae also told their husbands a month before the JFK Assassination.
Here's my theory: (1) The JFK plot was coordinated by the Dallas group known as the "Friends of Walker." (2) The "Friends of Walker" never published a membership list, but it was extensive group, covering many classes of Dallas Society and beyond;
(3) I will guess that Bill Randle was a member of the friends of Walker, and learned about the TSBD plot early, much as Joseph Milteer knew many details about the JFK Assassination two months in advance;
(4) Knowing about the role of the TSBD plot for JFK, and about LHO needing a job desperately, Bill Randle took this information to a Friends of Walker meeting.
(5) Since Walker had been tracking LHO for most of 1963, General Walker likely advised Bill Randle to instruct Linnie Mae Randle to put the bug into the ear of Marina Oswald who would push Ruth Paine to call Roy Truly. The rest would be history.