I am still working on sorting the Dan Hastings continuity out, but here's what I have so far.
From STAR COMICS No. 1 through 7, things are pretty straightforward. What we have in those issues is Dan Hastings appearing in both a 4- (or more) page heavily illustrated text story -- each of which is a complete story in itself -- AND in 2 to 4-page comic stories, which continue from one issue to the next. The overall title of this storyline is named in the first panel of the first strip, "Dan Hastings and the Demons of Mexady".
We are missing scans of STAR COMICS Nos. 8, 10, and 12, and here is where things begin to get confusing. Apparently the editor of Star Comics decided that having both the 4-page text feature Dan Hastings and the 4-page continued comic strip Dan Hastings was too much Dan Hastings per issue. Abruptly it seems, the Dan Hastings strip is replaced by a new feature (also by the same creative team of Ken Fitch and Fred Guardineer) called Don Marlowe. There are only 2 scans of Don Marlowe stories available (from Star Comics Nos. 11 & 13), but the characters and relationships of the Don Marlowe strip not-so-coincidentally parallel exactly those in the Dan Hastings strip. The storyline however, is a new one.
Adding confusion here is that the Dan Hastings strip also appears in a COCOMALT giveaway comic at this time, but the story is unconnected to to the earlier "Demons of Mexady" storyline which seemed to be abandoned when Star Comics abruptly replaced the Dan Hastings strip with Don Marlowe. The next comic strip appearance of Dan after the Cocomalt giveaway is in AMAZING MYSTERY FUNNIES Vol. 2 No. 5 (more than 2 years after the last comic strip appeared in Star Comics No. 7). Amazingly though, this seems to pick up the continuity of the "Demons of Mexady" story where it left off 2 years earlier. There are some differences, though. Even though the artist is still Fred Guardineer, the appearance of the villainous Earth-traitor Hanz Raskow (previously depicted as a caricatured obsequious Oriental-type) now appears as a Russian (or possibly Prussian)-type character. Other than that, the plot seems to carry on logically from what had gone before, but the difference in the character's appearance would seem to indicate that this story was newly-drawn, and not some mere leftover which had gone unpublished when Star Comics abandoned the feature earlier.
When Dan Hastings next appears in MLJ's BLUE RIBBON COMICS Nos. 1 & 2, not only does the strip reappear, but also the generous 4-page text feature Dan Hastings story (still a self-contained story). However, the Blue Ribbon strips begin an entirely new storyline for Dan Hastings. They acknowledge the earlier main villain, Eutopas of Mexady, and his previous (unfinished) plot to conquer Earth, but some time seems to have passed during which Eutopas suffered an unseen defeat (but of course, now he would like to revenge himself on Dan Hastings for spoiling his plans). Unfortunately, this new storyline goes nowhere after the first 2 issues of Blue Ribbon Comics (cover-dated November & December of 1939) -- that's the last we see of "the original" Dan Hastings (as far as I can tell) ...
-- Until 2 years later when the strip reappears in SCOOP COMICS No. 1, looking completely different in art style and story premise, apart from the characters of Dan, Dr. Carter, and his daughter Gloria and son Bob. Now the comic stories are self-contained, not continued from issue to issue. Eutopas and the Mexadians and Hanz Raskow are nowhere to be seen, and the flavor of the strip has completely changed now. This will continue in Scoop Comics until the March 1942 issue (No. 3), before it disappears again, not to be seen for another 2 years -- until it returns in DYNAMIC COMICS No. 8, first in a new story, and then reprints of all 3 episodes previously seen in SCOOP. Then it continues with new stories through Dynamic Comics No. 13, but then it disappears again. When it comes back in Dynamic Comics No. 18, it's in a condensed adaptation (with new art) of the original storyline, "Demons of Mexady"!! That only lasts for a single issue though, as by No. 19 it's back to being a pseudo-Flash Gordon clone for Dan Hastings, which continues through No. 21 (the final issue). Believe it or not, the Scoop/Dynamic psuedo-Flash Gordon Dan Hastings returned yet again, in re-titled reruns which ran in the back of St. John's ATOM-AGE COMBAT in 1953!!!