I’m pretty sure JPH (whom I’ve corresponded a little with in the past, though not on universalism) wasn’t charging that universalists are getting their universalism from Mormon doctrine.
I think I misunderstood the question in your topical title. Do Mormons really believe in post-mortem evangelization? Yes, at least some Mormons really do. Is PME typically affirmed by orthodox universalists? Yes, we do.
Is this universalist position “really” Mormon doctrine? When someone asks the question that way, I think in terms of transmission of ideas. For example, is Christian baptism “really” the criobolium/taurobolium ritual popular in some mystery religions? (In the criobolium, the initiate lays down on a slab beneath a suspended ram which is then cut upon so that the initiate is, loosely speaking, ‘washed in the blood’ of the ram. For the taurobolium, it would be a bull. Bulls were vastly preferred, but a ram could be used if cash was tight. Mystery religions weren’t known for trying to initiate poor people, though, as a rule.)
People who ask the question that way are trying to explain where Christians got our baptismal doctrine (or doctrines) from. The answer is blatantly, “no, Christian baptism isn’t ‘really’ the criobolium.” The two doctrines and practices are utterly distinct aside from some understandably similar language here and there–and even then, it was scholars of the old ‘history-of-religions’ theories, back in the late 19th and early 20th centuries who tended to import the language to make the few distant similarities look more similar. If anything, the syncretistic mystery religions came up with the practice as competition to Christian baptism–the evidence for criobolia is much later than evidence for Christian baptism being described as “washed in the blood” of Christ i.e. the Lamb.
Similarly, no the post-mortem evangelism doctrine as a Universalist position, isn’t “really” Mormon doctrine. But it also is “really” a Mormon doctrine, too. So is the Resurrection of Christ: orthodox Christians (including orthodox universalists) share that doctrine with LDS Christians, and with Unitarian Christians, too.
JPH’s article is worth studying to some extent in its own right insofar as it addresses the topic of to what degree some scriptural references may or may not be reasonable testimony to post-mortem evangelization. I’d be glad to see someone comment on it from that angle. (I’d do it myself if I had the time; and may still do so. )