> Did you like it when the SCOTUS threw out the claim Texas made against Pennsylvania's election laws because the claim had "no standing"? That will be the same situation if New York tries to sue the Texas organization
That's not how standing works. Texas v Pennsylvania was thrown out because Texas was challenging Pennsylvania's state laws on grounds of violating the federal constitution by violating the state constitution, and if that sounds like a squirrelly claim that has no legal basis, it's because it is.
NY suing the NRA is completely different. For starters, the NRA doesn't have any sovereign immunity you can work around. So what matters instead is whether or not a court can find personal jurisdiction over the NRA. NY's jurisdiction over the issues they're being investigated for is already established, I believe, and given that the events have already happened, moving won't change that. Instead, this is basically an attempt to evade the law by disestablishing and reestablishing itself and saying "well, you're challenging NY NRA, but we're TX NRA and that's completely different," which isn't likely to go over very well.
As a general rule of thumb, if you could plausibly describe your legal strategy with a clickbait headline like "One Weird Trick to Evade Legal Responsibility," then the courts are unlikely to actually agree with you.