The Zeppelin design was not the last word to be sure, but it did represent some real advances, notably in the matter of achieving large scale designs--much harder to do with pure pressure ships or semirigid designs of the type that actually emerged.
Anyway OP specifies Zeppelins.
And I don't see how stepping away from the rigid design helps enable earlier successes. Motive power is still motive power; at a given displacement volume with a given more or less streamline shape, you need the same power (assuming comparable propeller efficiencies) to drive it at a given speed. In addition to that, power rises as the cube of the airspeed. The aerodynamic forces acting on the body rise with the square of the airspeed. This determines the structural strength required. Indeed there are alternatives to making a rigid metal frame but they have their own drawbacks as well as advantages. As it happens, the ball has been moving toward the pressure ship court in the late 20th and 21st centuries, due mainly to advances in high tech fabric materials versus a slower pace in materials of they types we substitute for metal. But in 1890 I think the reverse would be true--the fabrics that innovators could work with were severely limited natural materials, subject to a great many drawbacks. Separating the outer hull fabric units, meant to withstand exterior aerodynamic forces and transfer to them to the rigid hull, from the inner volume gasbags, limiting the stresses they had to endure and enabling a choice of materials optimized toward successfully retaining hydrogen without worrying about other stresses such as standing up to high airspeed stresses, enabled the designers to arrive at least-bad solutions given the poor choices available.
Decades later, in the 1930s, Umberto Nobile was hired by Aeroflot in the Soviet Union, to develop airships for civil use in the USSR. He was not without his own pigheaded biases. He concluded that the mediocre success of his favored semirigid designs under his direction in the USSR had largely to do with Russian incompetence and superciliously advised the Soviets, as he was leaving, to focus on Zeppelin type designs since his own semirigids were allegedly too advanced for Russians to handle. However, that same decade witnessed the limited but to my mind still impressive successes of the American design for USS Akron and Macon, two rigids designed for helium inflation and nearly as large as Hindenburg, the ongoing success of the older Zeppelin products USS Los Angeles and the Graf Zeppelin, capstoned of course by the record of the Hindenburg itself. No nonrigid or semirigid design ever approached those giants in size nor in overall performance parameters.
If you want to beat the utility of the Zeppelin design you have your work cut out for you then, and I suspect that in 1890 you'd do better to attempt some sort of Zeppelin type design than fool around with allegedly simpler and lighter designs that actually put too much weight on organic materials of indifferent performance. Into the bargain--if you are a time traveler with secret access to a high powered computer capable of computational fluid dynamics analysis and other methods of brute-forcing calculations beyond normal human ability, you might do all right to fool around with pressure stabilized materials--otherwise, a huge advantage rigids had over other approaches was that the math of predicting stress concentrations could be greatly simplified via the rigid frames, enabling reasonable approximations to designs of adequate strength without being grossly overweight.
Indeed I think sloreck's ballpark estimates are correct. Broadly speaking, the same innovations that enabled aerodynamic flight were the same ones that enabled effective dirigible aerostatic flight. Power, and strength combined with lightness, were vital in each case, and airships are not generally speaking a form of flight that can be managed with primitive tech, no matter how many movie images love that trope.
The distinct advantage airships enjoyed over airplanes for a time was that making airships to large scale was feasible earlier, and that in turn enabled larger relative stocks of fuel and payloads, and thus approximated to an answer to the challenge of long range transoceanic scale ranges with decent payloads earlier. In military terms this meant larger warloads over longer ranges, but as wartime experiences proved this was more than offset by greater vulnerability due to being large (hence visible) and slow. The Germans went for high altitude to try and compensate, which ate into payload and exposed the ships to unforeseen high altitude winds as well as inadequately provided for foreseeable problems of oxygen depletion and extreme cold.
No matter what the design, pre-1900 airships would be dangerously slow, and fragile. Inability to maintain a given airspeed puts the ship at the mercy of winds faster than its maximum speed and renders them impractical for revenue service, being too dependent on winds to rely on.
IMHO, the window for commercial success of airships on a large scale was the 1920s. No earlier. It is my belief, more of a hope, that if airships were established in the '20s then come the challenges of the 1930s there would be adaptions that keep them in the game in a changed role and thus to the present day, but that is highly speculative.
