LAX-HNL-LIH 11/02/18. Bid $300. Several days later was offered the "opportunity" to bid higher, but opted to stay at $300. I don't recall the minimum bid, sorry. I just got the email accepting my offer. I suspected I was going to get it because there were five first class seats open as of yesterday. This morning two were gone and I hadn't gotten an email with a response yet, so my guess was that they were waiting to see if anyone was going to increase their bid. Maybe not, but I'm happy at $300 a pop.
As a side note, yesterday was the first day a seat could be chosen. Up until then, their was an error code when attempting to view the seat map. HA customer service said the aircraft hadn't been determined, hence the wait. I thought that was unusual. I hoped it would be the A330, and it is. All the flights I've seen from LAX-HNL are the A330, and I was glad that remained the case.