The problem is that you’re conflating two issues that should be separate: paywalls vs article/source quality.
The article posted on HN should be the best generally-accessible article on that topic, end of story. In this case, if the Forbes article is better, that's the one that should be here. If the NYT version is better, that's the one that should be here. If they're about on par with one another, then the first one to be posted and upvoted should remain, as nobody would want a norm in which the moderators unilaterally change a submission to a different source from what was originally submitted and upvoted by the community.
If it has a paywall, the only question is, is there a workaround that would allow anyone to access it. In the case of the NYT, the answer seems to be yes; you just need a browser instance that hasn't exceeded the NYT's monthly limit. I haven't heard anyone ever say it's impossible for them to access NYT content. Just sometimes inconvenient, if you need to open a different browser window. For me, if I'm on mobile, that might mean switching from my usual Chrome instance to Safari or Firefox. But I've never found a case where I can't access it. It's a little inconvenient, but it's OK. Other people have different standards of convenience. E.g., some people disable all Javascript and get annoyed that a site won't render for them. So you can never meet everyone's standards.
I totally understand that you're well-intentioned and are wanting to find a solution that is best for the broader HN community.
But please understand that those of us who have been on HN a long time (12 years in my case) have seen this topic thrashed out repeatedly (sometimes multiple times per week). We've all discussed an thought about it enough that we understand that the policy the HN mods have arrived at and written into the guidelines is a variant of the old adage: the worst form of government, except for all the others.
Other policies would lead to scenarios in which there are arguments amongst the community and mods over whether an arguably-slightly-less-good-but-non-paywalled version should be favored over an arguably-slightly-better-but-weakly-paywalled version. Or alternately, any sites with paywalls, even porous ones like NYT, should be banned altogether. None of these outcomes are clearly better than the one we have.
I know imperfect solutions are hard to stomach sometimes!