Need help selecting stepper motor and controller

I have constructed an 8ft tall moving bookcase/hidden door that rolls on wheels on a cement floor. I have already constructed guide rails that keep it from "walking" in and out. I have connected steel cables to the top and bottom - one set to pull open and one set to pull close. With pulleys I have directed these two pairs of cables to a common point (in the attic) where I plan to mount the motor. The cables come straight up vertically to the motor position. My though was to use chain on the motor and connect the cables to the end of that chain (I have attached turnbuckles to the cables to enable adjustment).

As I said I have already constructed this and using a pulley and weights in place of the motor have measured that it takes 32lbs to move the door in each direction. The door travel is about 46-48 inches. I would think I would like it to open in about 3 seconds. As this bookcase will have some fragile things on it I would like it to start slow and accelerate.

So while I am a newbie at this I am a software guy who has an EE degree from 40 years ago so I can handle the math but I need some help on where to start. I have tried a few stepper sizing programs and it seems that a belt drive with a 90 degree orientation makes the most sense. But...

I am not sure how to decide on direct or geared drive etc, Where should I start?

Thank you in advance.

Applying 32 pounds force (~140 N) over 1.2 m for 3 seconds is about 60 Watts, which is unrealistic for a stepper.

Consider using a brushed DC or AC gearmotor instead (suggest 150 Watts minimum), with limit switches, or use less power and take a more realistic length of time to move the thing.

But much more importantly you need to consider safety. You probably should have a current limited
supply for the motor to ensure the forces involved are inherently limited to just enough to move it.

Better still have current monitoring that shutsdown the system if the motor pulls more than the expected
current for more than some time limit. Apart from anything else this can prevent the motor overheating
if it stalls for some reason.

A stepper is entirely unsuitable for this application, and would be inherently unsafe too.

Suggest you post a drawing of the gear train/pulley arrangement

if you are doing belts and pulleys, a driven pulley might be 3 times the size of the drive pulley.
if connected direct drive to the motor, the motor would spin less than one revolution on a 90 degree swing of a door.

a triple stack, NEMA-32 would be limited to less than 400 inch pounds, so the driven pulley (on a 2 pulley set)would need to be rather large. consider that you would need to have 5 or more teeth engaged in the drive pulley, that means 20 teeth, and on an XL belt, your 60 tooth drive pulley would be about 6 inches in diameter (McMaster Carr)

if you used a motor that had a gear head, say 10:1 you would get some multiplication of forces, even with the loss of efficiency.

a worm gear system would offer some advantages, smaller motor, higher motor rpm, etc.

Since stepper motors miss steps when the forces exceed their ratings, I do not see the ability of a stepper to exert more force than any other type of motor.

But regardless, you are out of the realm of hobby motors and into the arena of machine tools.
And that does bring up the safety issue because of the forces involved.

Clutches to allow the door to swing and not crush your hand or a child would be in order no matter what drive you wind up with.
Guards like on elevators to prevent damage when a thing is in the way...

as a note, steppers do make noise, they whine when in use. the drive would not be quiet.

lastly steppers have no power when turned off. you would not want to leave the unit powered, so a separate locking mechanism would be needed at both open and closed. if you used a worm gear, the leverage of a human pushing on the door could destroy the drive.

Seems like we are offering more warnings than help !