Let's try and put it all together. For the purpose of this exercise I'll assume that the killer did in fact come down the stairs immediately after the shots. I'll refer to the shooter on the 6th floor as "Oswald"
12.30.00 Last shot
12.30.30 "Oswald" arrives at the stairs on the 6th floor
Adams and Styles arrive at the stairs on the 4th floor. Dorothy Garner sees them go down the stairs
Officer Baker arrives at the front entrance (seen by Lovelady) and meets Truly, after just parking his bike
Shelley and Lovelady are in front of the main entrance of the building. Gloria Calvary tells them the President has been shot.
They first go to the little traffic island in front of the TSBD and then decide to go towards the railroad yard
Lovelady and Shelley see Truly and Baker entering the building
Mr. BALL - Then what happened?
Mr. SHELLEY - Gloria Calvary from South-Western Publishing Co. ran back up there crying and said "The President has been shot" and Billy Lovelady and myself took off across the street to that little, old island and we stopped there for a minute.
Mr. BALL - Across the street, you mean directly south?
Mr. SHELLEY - Yes, slightly to the right, you know where the light is there?
Mr. BALL - Did you see Truly, Mr. Truly and an officer go into the building?
Mr. SHELLEY - Yeah, we saw them right at the front of the building while we were on the island.
Mr. BALL - While you were out there before you walked to the railroad yards?
Mr. SHELLEY - Yes.
Mr. BALL - By the time you left the steps had Mr. Truly entered the building?
Mr. LOVELADY - As we left the steps I would say we were at least 15. maybe 25. steps away from the building. I looked back and I saw him and the policeman running into the building.
12:31.00 "Oswald" arrives at the 2nd floor and goes into the lunchroom after decending 4 flights of stairs
Adams and Styles arrive on the first floor, after decending 3 flights of stairs, and leave the building through the loading door
Truly and Baker, somewhat delayed by trying to call an elevator down, pass the elevator block on the first floor and
run towards the stairs, just missing the women
This timeline demonstrates that if "Oswald" and Adams & Styles both arrive at the stairs 30 seconds after the last shot and they descent the stairs at roughly the same speed, they could in theory have been on the stairs at the same time, with "Oswald" arriving on the 2nd floor around the same time Adams & Styles arrived on the 1st floor.
12:31.15 Baker arrives on the 2nd floor (Truly is already climbing the stairs to the 3rd floor) and meets Oswald in the lunchroom
Adams and Styles arrive at the North East side of the loading dock and go down the stairs
12:31.30 Adams and Styles have gone round the most Northern point of the loading dock and start running toward the railroad yard
12.33.00 Adams and Styles are stopped by a police officer who tells them to go back to the building.
The women walk along side the railway track to the front of the building.
Shelley and Lovelady are in that same location
Mr. BALL - Shelley and you went down how far?
Mr. LOVELADY - Well, I would say a good 75, between 75 to 100 yards to the first tracks. See how those tracks goes---
Mr. BALL - You went down the dead end on Elm?
Mr. LOVELADY - Yes.
Mr. BALL - And down to the first tracks?
Mr. LOVELADY - Yes.
Mr. BALL - Then you came back. How long did you stay around the railroad tracks?
Mr. LOVELADY - Oh, just a minute, maybe minute and a half.
Mr. BALL - Then what did you do?
Mr. LOVELADY - Came back right through that part where Mr. Campbell, Mr. Truly, and Mr. Shelley park their cars and I came back inside the building.
Mr. BALL - And enter from the rear?
Mr. LOVELADY - Yes, sir; sure did.
Mr. BALL - What did you and Billy Lovelady do?
Mr. SHELLEY - We walked on down to the first railroad track there on the dead-end street and stood there and watched them searching cars down there in the parking lots for a little while and then we came in through our parking lot at the west end.
Mr. BALL - At the west end?
Mr. SHELLEY - Yes; and then in the side door into the shipping room.
12.34.00 Adams and Styles arrive at the road that runs parallel to the TSBD.
12.35.00 After walking the distance from the warehouse building next to the TSBD, Adams and Styles arrive at the front entrance of the building
12.36.00 Adams hears a radio report about the shots having been fired from the TSBD building.
Adams and Styles enter the TSBD through the front entrance and take the stairs to the 2nd floor,
Adams walks through the office space to the North West corner and takes the freight elevator to the 4th floor.
Shelley and Lovelady enter the building at the back and Lovelady - according to his testimony - sees a girl
Mr. BALL - You came in through the first floor?
Mr. LOVELADY - Right.
Mr. BALL - Who did you see in the first floor?
Mr. LOVELADY - I saw a girl but I wouldn't swear to it it's Vickie.
Shelley only saw Eddie Piper
Mr. BALL - When you came into the shipping room did you see anybody?
Mr. SHELLEY - I saw Eddie Piper.
12.37.00 Harkness seals off the building
The times are approximations, but the timeline works perfectly and includes all the known information without any witness having to lie.
I challenge anybody to come up with a similar timeline that starts with Adams and Styles leaving the 4th floor 4 to 5 minutes after the shots and still incorporates all the available information correctly.