The Haertel History.
By summarizing plot elements and background details, I have made four works, with some input from a fifth (see below), sound like a much longer Heinleinian future history with successive interplanetary and interstellar periods.
Haertel's anti-gravity device is not fuelled whereas the DFC-3 is. Therefore, the Haertel overdrive is not merely an interstellar application of Haertel's anti-gravity. The latter is his theoretical and practical discovery of the late 1980's whereas the former follows from his theoretical discovery of 2011 according to one of the Jack Loftus/Heart Stars novels. The Haertel and Loftus timelines diverge at some point which may be after 2011 in Terrestrial history but has to be much earlier in terms of galactic history because Loftus' galactic center is occupied by the ancient Hegemony of Malis, not by any telepathic "Central Empire."
There are similarities but also differences of which some can be incorporated into a single timeline whereas others cannot:
Loftus and his colleagues serve a UN world government in the mid-twenty first century, not a Matriarchy in the further future;
Like a handful of Matriarchy diplomats and Marines in that alternative future, Loftus and two other Earthmen make a long journey home to warn of a threat from a heart stars civilization;
their FTL drive is not a Standing Wave that has replaced the Haertel and Arpe drives but a modified Haertel overdrive that is called "the Standing Wave;"
Loftus' mentor refers to Garrard's strange temporal experiences with the Haertel overdrive Mark I;
an "Angel" allied to the UN informs us that Earthmen have withdrawn in confusion from the Centaurian beadmungen.
Thus, even a novel set in an alternative scenario imparts some information about the primary Haertel timeline.
Having introduced and defined a galactic conflict between telepaths and their natural opponents, Blish saw no reason either to recount or to resolve the conflict. This sequence of stories would have been extended only if some later story idea had required a reference to the Matriarchy or to the Central Empire just as the story introducing them had required a reference back to Arpe's discovery of microcosmic telepathy and as Arpe in turn had referred back to Garrard as the first man to reach Alpha Centauri.