I'm no expert, but I would say let the tree do what it wants to do. If it was doing too poorly then it wouldn't be flowering.

The inflorescences don't photosynthesize so they are doing nothing positive for the palm, and it is drawing energy from badly depleted resources to produce them. My "Bulgarian" likewise produced several inflorescences, but I removed all of them in hope of directing its energy towards producing new foliage instead.

I am not an expert on the subject, but could the greenish color to much of the young inflorescence indicate that some photosynthesis can/does occur? I would be tempted to just leave it alone personally, but I understand what Johnnie is saying.