Barring an actual agreement between the NHL and PA in the next week, I think that that we will lose his signing rights on June 1st. Sucks for the handful of teams impacted, but I don't see a compelling legal argument that the NHL should be able to unilaterally amend the league's CBA to benefit teams just because a different league changed their eligibility rules in a way that gives players more career options.
NHL teams had the ability to sign these kids for 2 years. They either weren't willing to pay the signing bonuses required to do so or the players decided that they would forgo making 6 figures in order to keep their career options open. The fact that the players gained a career option that the league wasn't anticipating (or failed to prepare for) isn't really a compelling reason for the league to be able to change the rules of a Collective Bargaining Agreement without bargaining with the players collectively.
I'm very rarely on the NHL's side when it comes to CBA negotiations, but I think that this is an issue where it is probably in the PA's long-term interest to give the league a 1 year temporary resolution to extend signing rights for these players by 1 season. It's half a dozen total players that aren't even union members yet. One was drafted in the 4th round and the all were drafted in the 6th or later. I understand that you always want to get something back in a negotiation, but realistically the league doesn't care enough about a few teams losing signing rights to late round picks to offer anything of substance. CBA negotiations are reportedly going well and this would be a pretty low-sacrifice olive branch for the PA to give up.