Not worth it.
A cubic foot of uncompressed hydrogen at room temperature has around 270 BTUs
A cubic foot of diesel has around almost 1 million BTUs
Not the right way to figure at all. The weird requirement of an airship, not familiar to people dealing with airplanes, is to stay in trim. If you launch with the right amount of hydrogen to lift payload plus all the fuel, as you fly, burning up conventional liquid fuel, if lifting gas remains the same the ship will be increasingly out of equilibrium, with more lift than weight. It can use aerodynamic lift (negative in this case) to counteract that, and it is always possible to simply vent lift gas as well.
But hydrogen, though far cheaper than helium, is still not free. It takes energy in one form or another to make it, and the notion of burning some hydrogen instead of simply venting it for added return on value was attractive. It also involved some extra risks so it was not casually done, but research was undertaken.
My point here was to skew the interest in developing relatively lightweight diesel engines further. As I noted, other motives to develop aero-diesel, not just for airships but for airplanes too, also existed. I would imagine hydrogen can also be introduced into Otto cycle engines with similar benefit, but the research I read about was for diesel.
A cubic meter of hydrogen displaces at sea level about 1.225 kg of air, at standard conditions, and itself masses 85 grams thus providing 1.14 kg lift. If then with every 1.14 kg diesel fuel, we also burn 85 grams of hydrogen, we get extra power versus just burning the diesel fuel alone--another way to put it, we reduce consumption of diesel per each horsepower-hour of output by a certain fraction. Your point is to defeat the argument that hydrogen is a good fuel by pointing out the tremendous cost of storage--even as a cryogenic liquid hydrogen requires absurdly large volume of tankage, which also is extra troublesome for having to be a fantastic insulator and because the absolute temperature it is stored at is very close to absolute zero, very hard to manage on a planet whose average temperatures even at altitude are above freezing water around 273 K. Gaseous hydrogen storage sidesteps cryogenic issues but costs us tremendous volume! It is clear why people say "hydrogen is the fuel of the future and always will be!" (also of course it is not "fuel" in the sense that we cannot simply mine or otherwise extract it, it must be synthesized and is really an energy storage medium. Diesel and petrol on the other hand are dug out of the ground and moderately refined.)
You see I am familiar with the drawbacks of hydrogen that typically negate its isolated virtue (not the only one, but pretty near) of having great energy potential when oxidized in air per mass unit which you rightly discount--in most cases.
But you are ignoring that the airship is hauling around a lot of hydrogen anyway; the storage costs are necessarily already covered. With storage for "free" as it were, why not take a new look at the possible utility as a fuel as well? Let's not let dogma or polemics blind us here!
In terms of energy released by combustion per mass unit, hydrogen has triple the specific energy storage relative to oxygen combustion of gasoline, which would be similar to diesel. (Diesel is a bit better overall in practice due to being more efficient thanks to higher compression ratios, but this applies equally to hydrogen, at least in small quantities, as to any other fuel). The added punch of extra combustion heat released by burning 85 grams of hydrogen is thus worth 255 grams of diesel fuel, more or less. So, if we scale the air intake up enough to account for the extra net fuel we bring in by adding the hydrogen, we would get the net output of 1.4 kg of diesel while actually just burning 1.14, for each cubic meter we deflate the hydrogen bag to maintain net trim at zero. This means that by consuming diesel fuel at a reduced rate with the proportionate amount of hydrogen induced into the air intake, we increase endurance and thus range of such an airship on a given quantity of diesel fuel by 28 percent! Call me crazy but that looks like a rather significant savings of fuel cost and extension of range to me. In order to stay in trim otherwise, it would be necessary to vent the hydrogen in any case, so this comes at no added operational cost.
There are extra risks involved in leading a flow of hydrogen down to the engines to be taken in of course, risks of creating a path to ignite the lift hydrogen specifically. This is a question of engineering though.
I note that this is a special case. It would not make sense to fuel the engine with 100 percent hydrogen--at any rate this is unlikely to be cost-effective considering the great difficulty of keeping liquid hydrogen in realistic conditions on Earth. Despite a drastic reduction in overall fuel mass, the hassle and great bulk of the tanks would be a serious drawback.
But it was something the Zeppelin designers, and Americans later, took quite seriously and with 30 percent performance enhancement in prospect I think you can see why. It might be a red herring in the matter of biasing engineering talent toward diesel engines perhaps, but you attacked the general principle on grounds that in context are quite mistaken.
The alternative to venting (and in this case getting a valuable second use out of the otherwise wasted vented gas) to stay in trim would be to somehow gain weight in flight to compensate for fuel weight consumed. (Yet another is to develop a mix of fuel molecules that overall has the same density as air, and burn that--tried in the Graf Zeppelin and in an American research blimp. But this is really the same thing as burning a mix of lighter than air gas and heavier than air fluid as proposed). The most reliable method hit on was water recovery from exhaust, a procedure that involved a number of hassles and lowered useful engine output power. Despite the hassles, not only did a number of American airships develop the option with more or less success, the Germans too were planning to use it in the Hindenburg and its successor, hoping to get access to American helium, and suitable apparatus was developed. You see, this trim problem is a big deal on airships and the favored solutions for small airships involving taking off heavy and using aerodynamics to compensate (venting helium is very expensive) don't work so well for larger ships, and a lot of effort went into resolving it. Sipping off the hydrogen gas for added engine power was a very attractive one and since in the time period I am talking about I don't think sufficient helium would be available to serve the airship fleets, I think this one would be highly favored. Note that enhancing engine combustion with a little bit of parallel hydrogen burning enhances the percentage of water exhausted, thus a ship equipped with moderately capable water recovery could supplement hydrogen burning with water recovery to gain net weight quite rapidly--in this case we would at least consider raising the fraction of hydrogen burned even higher so we are disposing of more lift than we are burning diesel fuel, and also gaining water weight. In that case the limit would be how much hydrogen you can include before changing the chemistry of diesel combustion too much for the engine to run well--empirically that limit was around 90 percent! Vice versa if there were a need to increase lift quickly, switching over to pure diesel fuel burning combined with dropping water ballast (knowing we can get water ballast back quickly later by burning lift gas as fuel--every 85 grams of hydrogen will yield many hundreds of grams of recoverable water, depending on efficiency of the recovery gear), and an integrated system of diesel engine that can switch between say 75 percent hydrogen consumption with water recovery and pure diesel fuel operation would be highly desirable.