I'd rather have a token system than relooting or picking drops tbh.
Something like an allagan token collected after each boss kill which would allow you to buy a gear piece dropping from a boss you already killed.

Let's say something like 8 tokens for a small part (accessories/belt/shield) 12 for a medium (gloves/head/boots) and 16 for a bigger one (chest/legs)

Ofc weapons wouldnt be buyable since you can already get poetics ones.

This system would allow you to overcome the RNG and be quite fair imo (2-4 times a full FCoB clear for a part). The main point would be that you can only buy parts dropping from boss you already have killed