Drywall – Centering the bed on a 12″ post protruding from a wall

if the post is within the line of the walls:

Blue is existing, red is nailing strips, green is bulkhead...

You would certainly need to consult a structural engineer and get all plans approved and permitted before beginning work. It will be expensive but since you indicate willingness here goes.... It is completely possible to relocate that post. The question will always be price and design. In my humble opinion the work isn't even all that difficult once you know exactly which material and sizes are required for the load.

That support post is compression support for the visible beam. In order to properly move it you would likely need to add two vertical support beams with a perpendicular cross member to take their place. This member would likely be steel.

That new beam could go below the existing beam (with the existing beam sitting atop it) but depending on the span and the load this would fill in significant headroom and break your clean ceiling line.

Alternatively, depending on the roof structure, you may be able to hang the new beam above the visible beam inside the attic space. This would have the added benefit of not eating interior headroom. You would probably place the vertical beams inside the wall where the bear painting is, and the wall to the left of the sink.

Either approach should work. Neither is significantly complex for a structural engineer. They will both likely be quite expensive to do.

EDIT: So how will they change it? What's involved? If you put the beam below the existing one, then temporary support posts will be constructed on both sides of the existing post. The post would then be removed and a replacement beam jacked in place beneath it.

If the beam is to be "hung" from a new crossmember then the existing post will stay in place while the new posts are built. The beam would be jacked up slightly from both sides, and a steel hanger bracket would be placed under it, fastening it to the new in-ceiling beam. Finally, the existing post is removed.

In both cases a support immediately below the beam, beneath the floor, should give support all the way to foundation which means that you may need to pour in the crawlspace and tie into the existing stem walls.