Would HMA No.1 being equivalent to the later airship R.36 design have helped the program?
As I've already pointed out it could not have been done because (to paraphrase Oscar Goldman)
"We didn't have the technology" to build an R.36 class airship instead of "Mayfly".
If
"We'd had possessed the technology" an equivalent of R.36 would have been considerably more expensive than "Mayfly". R.36 was about three times larger (2,101,000 cubic feet v 663,518 cubic feet) and had five engines producing a total of 1,570hp and "Mayfly" had two engines producing a total of 360hp.
I don't know if there's an airship equivalent to the
"steel is cheap and air is free" theory for warships but in case there is I'm going to be prudent and say that an R.36 type airship built instead of "Mayfly" would have cost about twice as much instead of three times as much.
Therefore, a more realistic course of action that the committee that recommended the expenditure of £35,000 on one airship in the "real world" recommends the expenditure of £70,000 on two airships in "this timeline".
HMA No. 1 "Mayfly" would still be written off in September 1911. However, the second airship HMA No. 2 "Dragonfly" would fly a year later. It would effectively be the equivalent of HMA No. 9 and do what that airship did in the real world 1912-13 instead of 1916-17. Therefore, the development of rigid airships in this timeline would effectively be 4 years ahead of the "real world".
That might lead to the Admiralty ordering as many as ten equivalents to the HMA. No 23 and 23X classes in 1912-13 instead of the three rigid and twelve non-rigid airships that were ordered at that time in the "real world".
In the "real world" two of the three "rigids" (Nos. 14 & 15) were cancelled outright in the autumn of 1914 and the third (No. 9) was suspended. As far as I know this was because the war was expected to be over before they could be completed and because these were experimental rather than militarily useful airships.
In "this timeline" construction of these airships aught to proceed faster than the dirigibles ordered 1912-13 in the "real world". This is because Vickers design team and construction crew hadn't been disbanded after the destruction of the Mayfly so they could start to design and build the new airships sooner. Therefore, it's plausible that a handful would have been completed by 4th August 1914. If that's correct construction of the remainder would be far enough advanced to justify completing them on the ground that they would be available before the war was expected to end.
If that did happen I think more airships of the 23X type would be ordered once it was clear that the war wouldn't be over by Christmas. They would be constructed instead of the non-rigid airships that were produced in large numbers in the "real world".
A one-to-one substitution wouldn't be possible but my guess is that one rigid could do the same work as several Sea Scout and Coastal non-rigids. For example I've read that the non-rigid airships could only spend a few hours on patrol due to crew fatigue which was attributed to the open gondolas. However, the rigid airships had enclosed gondolas so the crews didn't succumb to fatigue as quickly and their larger crews allowed spare lookouts to be carried so they could operate a "watch" system.