In my personal capacity, I would submit that the most logical reading of Article 2, Section 2, 1-3. of the Constitution is that it applies as of the time the vacancy is created, not at some later juncture.
Laki resigned from the Senate Seat at 11:29:42 AM Eastern, before his deregistration at 11:30:23 AM Eastern. Therefore, at the time the vacancy was created, the HI Party was still a major party with 3 members, and therefore the responsibility for appointing a Senator was with the party executive, regardless of whether the party fell under major party status for a time at some later point. There was no party executive, therefore it fell to the party to elect one and then have that executive select a candidate. The executive was chosen by a majority of the members of the party and the executive appointed someone who was part of the party at that time.
I would remind the court that its precedent is to not involve itself in internal party deliberations, see Tack50 v Wulfric (2019):
https://talkelections.org/FORUM/index.php?topic=436487.0 . People may not like the fact that the HI party had no established bylaws or chair, but it simply did not. People may surmise that ReallySuper had powers based on being the 'founder', but the constitution does not recognize that, only an 'executive', of which the party simply had none. People may not like the fact that a majority of members of the party during the raid did what they did, but the fact is there is nothing in the constitution or in the non-existent HI bylaws to prevent it, and therefore the court has no role to do so.
Thus, I would ask the court to deny the injunction and dismiss the case with full prejudice.