Where do you live? Is it an urban loft that has this type of thing common in the area? Or do you live in a suburban single family home where you don't see this? That would depend on if leaving the exposed ceiling is a do or don't.

I live in an 140 year old farm house in the country.

Sheetrock it and add in some beams afterwards...??

Ironwood Builder, that sounds incredible. Would you by chance have a pic to reference? thanks

Bulk your bulkhead up, finish the edges and paint it a bright high gloss color, think true yellow or bright red-orange, to pop out your beautiful industrial beams and make it look like a design element. You could carry this color through on the perimeter headers for continuity and even run it down a support column to give some visual separation between living spaces. Don't over-do it, think visual surprise in a few well-placed spots. Make sure to finish your surfaces for a purposeful look to your design.