I would clearly agree that the view of the resurrection and the afterlife in (full) preterism is like in some manners to that of the Gnostics, not too unlike the Jewish (e.g. Philo or 4 Maccabees) and Christian Platonists, or even the Stoics, or the Sadducees for that matter. But I do not think a similarity in a point of doctrine is the same as dependent theological formulation. (I remember on this point the attacks on Calvin and Calvinism as importers of Stoicism because of some theological similarities and Calvin's interest in the likes of Seneca.)
But of course the dissimilarities with the likes of Gnosticism are huge. And I'm not sure one could point to Bultmann and (a very different thinker) Schweitzer as a source for King's inspiration. I have not read anything by him (King), but I hope every learned layman would digest both of the aforementioned scholars, particularly to understand the important developments of Bultmann's existential approach and demythologization as well as Schweitzer's 'Quest' and (after Weiss) consistent/apocalyptic eschatology, which in some ways has come closer to winning the day, helped along by post-Bultmann scholars like Kasemann (a disciple) and Cullmann (following in Schweitzer's chair) who proposed alternatives to Bultmann (the latter a proto-Wright on Christ as the center of history, though Cullmann's achievements may still outshine Wright's to date).
But now I am rambling. I believe the more clear path of inheritance of full preterism is 1) the sincere attempt to be faithful to the time texts' of scripture according to a fairly conservative hermeneutic, and 2) the work of preterists in the 19th century (many of them conservative) and (ironically largely Reformed) partial preterists in the later 20th century who have gone before and a) laid a foundation for believing the entirety of the NT was composed prior to 70 AD (importing the work of some liberal scholars like J. A. T. Robinson) and b) crafted an apologetic for interpreting the expectations of the NT in purely spiritual categories (as you note concerning enlightenment thinking).
Obviously, I (and I'm no scholar, I'm simply riding the consensus of scholarship) think that preterists - partial and full - are wrongheaded on all of the above mentioned accounts, but I do not think it is a clear issue of theological inheritance from liberal scholarship. The (full) preteristic doctrine of the resurrection becomes an apologetic answer for texts that prove very difficult to the system. Every system to some degree must do this. Of course, I feel the hermeneutical gymnastics being attempted in many places in the NT - because of their tensions with the time texts - in favor of the full preterist interpretation should instead give us pause to reflect upon the apocalyptic undercurrent of imminence texts in the NT and question such a literal(istic) interpretation of those passages.
One of the more notable developments in critical (as well as conservative) scholarship over particularly the last 50 years or so (but it started in the early 20th century) was an acknowledgement of the high degree to which apocalyptic provides a backdrop to much of the NT, including the belief in the physical resurrection, the use of escalated apocalyptic imagery for a church under (real and perceived imminent) distress, and a belief that the culmination of the ages and the return of the Son of Man could be very soon - all characteristics of Second Temple Judaic apocalytic. So, ironically, if the preterists followed the consensus of modern liberal and conservative scholarship (which I of course wish they and all preterists would do), they would be affirming as apostolic the doctrine of the physical resurrection and the anti-Platonic nature of Pharisaic and Christian 'life after life after death' in the renovated creation.
So, from my perspective, I would agree that there are reasons to reject full preterism, however I do not think that a perceived relationship to liberal scholarship is one of them. Thanks, Paul, for your contributions and thoughts.