My '70 vert should be near if not identical to your '69 so I cycled my top and took some pictures. The top is probably a little stiff since it hasn't moved since last October.
Here is the top with the roof latches released.
I have a glass window, but it shouldn't make any difference. I used the top dash switch to raise the top to the vertical balance point so you can see how the folds start forming.
Note the top folds shown above look pretty crappy, but it all works out in the end. I just jogged the dash down switch to get the top just past the balance point and then let gravity do it's thing. The top came to rest sticking up about 5 or 6 inches as the next photo shows. Remember, your top may not fall as far or that fast because it doesn't have the weight of a glass window to haul it down.
Normally I run the power pump long enough to "suck" it down, but for this demo I just left it for few minutes and gravity slowly finished the job. All the way down looks like the following.
Hopefully some of this helps.
Your roof guy's suggestion to unzip the window is a crock, never done that on any vert I've owned, well that's a lie, I did it once to see how it worked and had a ***** of a time getting the zipper closed again.
I would wait for a hot day and put the car in the sun to really warm up the top, then use the dash switch to power the top down and keep your finger on the button until the pump can't move it any further.
A tip avoid raising or lowering the top when its cold, the material just gets too stiff. If you've run around all day with the top down and try to raise it that evening long after the sun has gone down you'll have a battle to get the latches locked.
Hope some of this helps.