Do Grammatophyllums root from stem cuttings?

[estación seca]

I have a small Grammatophyllum speciosum that came in late 2015 in a 6" pot. It had one old leafless pseudobulb, the next old pseudobulb with a full complement of leaves, about 3 feet / 90cm tall, and a new growth about 10 inches / 25cm tall. While I was out of town for a week in late March, I had it outside. It was nice and warm that week.

On my return, it looked like something had taken a large bite out of the base, where the most recent growth was emerging. That new growth was rotting at the base. It smelled pretty bad, like rotting plant material. I cut off the new growth, and found the rot had spread through all of it, so I threw it away. I removed the whole plant from the pot and washed off all the medium, allowing the roots to dry. They are not mushy and wet; they are dry and light brown, but I can't tell whether they are alive. They look almost exactly like Cymbidium roots. I have kept the plant bare-root and wet the roots daily, letting them dry in between.

The previous pseuobulb was also partially rotten at the base, but trying to make another growth from the side opposite the rotten new growth I cut off. I cut out what rot I could, but it kept spreading, and the new growth just pushing out died. I cut that pseudobulb off well above the rot zone. Now I have the top 8 inches / 20cm or so of that pseudobulb. The cut end has dried and the rot has not spread on this bulb after over a week.

The oldest pseudobulb is still intact down to the roots. I am hopeful the rot will not continue spreading, and this old pseudobulb will push another growth.

My question concerns the pseudobulb I cut off well above the base. If I lay it sideways in some barely-damp medium and keep the humidity high, is there a chance it will make new growths from the leaf axils?

Thanks.