This is a very well-considered post. However, I tend to believe you have overestimated the ability of the British to emulate German Zeppelin technology - or to develop their own industry. I know that OTL is different from this TL, but arguably, the British never built any rigid airships that were reliable or effective without directly copying German designs - designs that would not be available without downed airships to study in WW1 or obtained as war booty. On the otherhand, as you point out, Britain, more than any other nation, had the real need for large airships to establish commercial air links in the Empire, and provide a scouting force for the RN.
OTL, Barnes Wallis at Vickers did pretty well with hands that were largely tied. The key to success for the British might have been delaying the war, and for the faction in the Admiralty who were looking with some alarm at German progress in the field to quietly promote the development of commercial rigids by concerns like Vickers, as ostensibly private ventures (with some quiet Admiralty funding) as a means of testing and expanding British capability.
If a British commercial line to the East and/or South Africa and to Canada or New York could be successfully launched, then there might be action on purchasing a few of the hulls from the company for Naval use, as scouts and conceivably scout aircraft carriers, and as fast (relatively!) means of physical communications with ships at sea.
By the way, if one considers how hampered the British efforts were from above OTL they did not do so badly. One of their ships managed a transAtlantic crossing shortly after WWI; unlike the Brown-Alcock Vickers Vimy biplane that beat them to the record of first aircraft of any kind to do it by mere weeks, the rigid managed the crossing in both directions (starting with the difficult east-west journey) without crashing (as the Vimy did on landing in Ireland); it went a greater distance, from somewhere in eastern England all the way to Long Island and back again versus the Vimy's ultra-short Newfoundland-Ireland crossing, and it carried a significant payload of crew and passengers again both ways (including one stowaway who only went west, being put off in America). That ship was arguably a "copy" of a wrecked Zeppelin, true. And some British extrapolations of what they could reverse-engineer from wreckage, defectors, and hostile Germans post-war were disastrous. But other innovations were sound (such as the practice of eliminating the complication of the weight-distributing "keel" and instead situating weights on the ring structures), and Wallis's designs in particular were both unique and successful.
What hampered them was undue dependency on Admiralty patronage; when the war started one might suppose this only helped as it would secure them some priority, but the countervailing demands of other war needs tended to override the experimental rigids. Furthermore Churchill, as Sea Lord, was one of those people who hated rigid airships (rigids tend to evoke either love or hatred in people for some reason) and he did what he could to terminate the expense. Post-war, Britain was of course in a bad way financially, and the reorganization of aircraft assets took them out of the Admiralty (where the program had friends as well as foes) and into a cash-strapped Air Ministry/RAF system. Much loss and delay resulted.
I hardly think it's a sure thing that a commercial program could go from being a barely-considered notion to an operational reality within 9 years or so from 1914. But I do think this route of development holds more promise, grudging as it is, than the reality OTL of development in wartime.
ITTL, if rigids are indeed established in transport service, and the Admiralty has acquired modified versions of these designs, I do think that in a mid-to-late 1920s context they could distinguish themselves both as transports and naval scouts enough to secure their institutional place.
I do like your point that commercial competition between the Zeppelin and Schutte-Lanz firms might have let both firms advance quicker than in WW1 and steal each others' innovations. The end result might be "zeppelins" that were very different from the zeppelin-derived types we know from our timeline.
I guess I did not make myself clear enough; surely competition will be a somewhat useful spur, but also the proprietary nature of the rival inventions, protected as they would be under peacetime civil law, would be a barrier to the rival firms sharing each other's innovations.
I also think you have downplayed the possible American role. In a TL where advances in airplanes are somewhat retarded, rigid airships would be very useful linking together a large continental nation and its (not insubstantial) overseas territories. Also, the US "monopoly" on helium would not be lost on US mlitary planners. Finally, the USA would not have been a member of the European alliance structure and might be able to negotiate deals with both Britain and Germany to keep abreast of airship technology abroad.
I'd like to imagine something equivalent to the "Great White Fleet's " early 20th century circumnavigation ... the "Great Silver Fleet's" airborne circumnavigation in 1923!
Don't bet too much on helium; OTL by the end of the 1920s the government procurement system (which relied on private firms to do the actual extraction) could barely keep one big rigid afloat at a time! By the early '30s they were briefly able to keep both Los Angeles and whichever ZRS ship was flying at the time going, and meanwhile all along a handful of blimps were being kept aloft (though one year in the later '20s, the Army, which had the blimps for the most part until the later '30s, generously gave its share over to the Navy so they could operate their rigids). By the late 30s the Navy (having acquired all the blimps in a reorganization) could contemplate keeping many blimps going and during the war the number climbed to something well over 100. But these blimps of course, though generally large by modern advertising blimp standards, were quite small compared to a rigid, something like a 20th their volume or less. By WWII I suppose if the Navy needed 4 or 5 or even 10 times the helium it did OTL that would have been forthcoming.
But in 1924? I doubt there would be even one helium-lifted rigid anywhere; if there were one I suppose it would be American. The reality facing everyone, including Americans, would be to either use hydrogen or not fly airships.
If there were this successful British venture I hope for, I don't doubt that Americans would extend it in cooperation (as a quid pro quo for making New York, and American destinations in general, available for the British lines, and possibly as a formal partnership) and have our own experience and expertise. In wartime I'd expect American hangars to produce a lot of the aerostatic tonnage launched by the Allied side. Even if the USA doesn't join, I imagine that as OTL we'd be "neutral" largely on the Allied side, and supply that side with materiel. By the end of the war, the number of USN and perhaps American-flagged commercial ships using helium will have risen from zero or one to say four or five, maybe ten. Meanwhile hydrogen-lifted ships will be flying in greater numbers. I hope.
Great American contributors to the aerostatic arts of OTL like C.P. Burgess would probably make themselves known and valued; postwar, Americans could lead the field.
But I just don't see the scope for their doing so before the war; helium frankly might prove more of a hindering will'o'the'wisp than a help.