Remove the border!!! I would add crown moulding to the in-square and add a beautiful chandelier that goes well with your new cabinets. This way, the crown moulded square surround looks like you we're purposely framing a beautiful chandelier. You could even paint it a grey, or different color to pop. See added photos.

Another photo I just seen...

Ok, I think the consensus is to not remove the bulkheads because of the beams. I will get rid of the border. I am a little confused but very intrigued about the idea of the crown molding. Another question would be whether or not I should paint all the wood beams, windows and door frames in this room. My hardwood floor will be sanded and refinished to match the rest of the house, which is a medium brown. The new cabinets will also be brown, just a little darker than the newly stained floor. Would it look ok to leave the beams, molding, etc., the pickled stained pine or should I paint. Thank you for all your help!!

Also, it was suggested above by amoora that pendant lights be installed (after taking out the fan, of course),which I would love to do. Unfortunately, our island extends beyond the bulkhead. The fan is only centered on the far end of the island, just above the cooktop.

Emily Hurley I am going back to your comment about the beam needing to attach to something. What would you think if I just removed the one beam that attaches to the bulkhead and leave the rest up? Would that look too strange? I would like to get new cabinets but do not want to go to that expense if I cannot remove the bulkhead. Thanks for your suggestions.