It's irrelevant to your timeline, with its POD half a decade after the Navy LTA program was shut down. Actually we'd need a timeline with the POD in the 1950s. The Russians have not done much with LTA. I was actually thinking of an American application. I just put it out there in case anyone (this timeline, or ESA, or Sputniks, or anyone else who wants to step into the ring) wanted to move big rocket stages around and was finding that airplanes couldn't handle the job.
I was thinking of someone remembering Goodyear's proposal (or in some 1950s POD timeline, its actual implementation for rockets considered big at that time) and thinking, aha, we need something like this but bigger!
"Blimps" might not cut it. Full disclosure--some years after this 1959 proposal, one of the Navy's ZPG-3Ws crashed off Massachusetts. There's some controversy about just what happened; in the enquiries afterward Goodyear blamed pilot error while the survivors of the crew said the fabric of the upper hull ripped open. The -3Ws were really pushing the state of the art. We could probably do a lot better today, with more modern materials. But with these big ships we might prefer to switch back to a rigid airship design. Coming at it with a clean sheet of paper, something about the size of Hindenburg (or the helium-lifted American rigids Akron or Macon, which were nearly as big) could manage a 50 tonne payload, considering weight savings possible with more modern materials.
Just looking at that Goodyear proposal I see it as quick lash-up Mark I at best; you'd think they'd want to at least fair over the gaps between the noses and sterns of the component blimps; from there it seems straightforward to fill that volume with more helium and lift more. There's some aerodynamic advantage to making a broader hull, if one is anticipating a lot of dynamic lift--indeed by the 1950s the Navy blimp operations routinely took off heavy and sometimes still had some excess weight when landing too. The last time I was thinking about this I was assuming a lot of the lift would be dynamic. So actually, if we could trust this thing not to split its seams in flight, it might have been up to hauling a Vulkan stage, as designed then. Nowadays I feel that if one wants an airplane, make an airplane; if one wants an airship, design it around its static lift capabilities, don't make it rely routinely on dynamic lift. A straight airship has the advantage that it has the same lift at any airspeed including zero.
But yes, it seems that, while there might have been some reasonable concern back in 1959 they couldn't manage it, that airplanes work just fine. Everyone who can think seriously about a space program of their own makes airplanes; all the first-rank potential space program nations have firms or their equivalent that have made some really big ones. With an airplane of course tonnage is not the problem, the problem is the volume of the load. That's not a big problem for the airships, that are so huge already anyway. But while it is a problem for planes, it's a problem that by now has been solved. Evidently no one is too worried about landing the load some miles away instead of right at the gates, and to be sure, an airship big enough to haul a 43 tonne Vulkan stage won't dock right at the gates either.
Hey, I'm trying to remember where I saw the proposal for a flat-bed jet transport. It looked like someone had taken a C-5 or the like and just crimped its fuselage down like a tube of toothpaste. The idea is, just load your awkward bulky cargo right onto the back, out in the breeze. Presumably one puts tarps on it and tightens them down real well with straps, but it's OK that there's drag, the engines have enough thrust to overcome it. This might work especially well for rocket stages, which are streamlined already pretty much; you probably don't even need the tarp!
(Your Evolved Apollo stages seem especially well suited to this approach, with their built-in attachment points and structural reinforcements for parallel first stages--just roll then on so one of those panels faces down, and bolt the thing onto the plane using it).
I still don't remember where I first saw the idea, but
here's the patent. It's a Lockheed design, the year was 1983. So assuming that the aero industry and the military aren't massively butterflied by the early '80s (and it seems that on the whole they aren't) the idea is, um, in the air right about "now" in ETS.
It seems like just the thing--a standard cargo plane for a standard rocket stage cargo! With DoD fingerprints all over it--Reagan ought to love it.
Nothing in the patent or the Wikipedia article on it says anything about the weights but the Wiki article does say it looks about the size of an L-1011, which in its earliest version had a take-off weight of 200 tonnes, a landing weight of 167, and structural weight of 102.
So if the length of the "bed" is long enough for the biggest rocket, it ought to handle the mass just fine, even allowing for degraded performance due to poor streamlining.