Instead of suspending it, you could consider building a loft?
You could get 8 foot 2x4s, cut them so that they reach just above the door frame, and then mount the platform you already have onto the legs.
It would mean you have to reach that high to get the HBOT every time, do you think you could lift down 35 lbs regularly?
Based on your photos, it looks like you have enough space for a loft, although you may need to move the shelf with clothes on in shown in post #5 on the left.
You could try a simple design like this:
This DIY workbench is simple enough and cheap enough that you can make it in a morning, and yet it's big enough for serious woodworking and hobby projects.
www.familyhandyman.com
However, it's usually a good idea to not just use horizontal fasteners (screws) to secure any load. The strongest design is supporting from the weight from the bottom with laminated legs and 'aprons'. Like this:
Pin For Later!
www.ana-white.com
Except you don't need the bottom shelf.
This plan above could use a bit of a change. Here's what I would do (but I'm not an engineer nor a carpenter):
I'd delete the bottom bit below the red line. You could skip the stubby legs, as you don't need a bottom shelf, and have your stabilizer aprons directly along the floor.:
The other thing about these pics is to change the orientation of the aprons to fit your storage space. They could all be in the orientation of the green check mark, giving a free path.
This is basically what I did to fit the HBOT in my bedroom, I built a loft bed to fit the machines under it.
Anyways, something to consider if the pulleys don't work.
