The "LM's cabin pressure vessel varied thickness" would in no way have protected crews from VAB radiation or solar flares or gamma radiation in space, even during what you might envision as a skillfully-timed, optimal-trajectory, brief transit. Ask a Russian space scientist why the Soviets or Russia never chose to risk VAB transit. Their belief consensus is that there's no publicly-known, adequate way to shield humans in transit.
What you may think you may know about the VAB data are not trustworthy. The data have been cooked and seeded with disinformation to keep people like us from questioning the claims about the Apollo missions. Clever try with the first-year engineering student insult. I also never said or assumed lead was the only effective shielding.
The "VAB hoaxer issue" as you call it, has not seen one living creature transit the VABs under a NASA or foreign coutry's space administration since 1972, thus, essentially for the last 50 years. Why is that? If we were to for a moment set aside NASA's Apollo mission astronauts, zero living creatures have transited the VABs in a NASA, Russian, Chinese or Japanese program in the history of the world! So it has not been debunked. Somehow, it was only doable prior to handing it over as a Muslim outreach, for that little window of time, when the mock-up set was available for photo shoots and filming.
NASA speaks of its Orion project as if they're years away from being able to send up a human in that. Why would that be after 30 grand Apollo successes?
Time fails, but another manifestation of the hoax a priori was the Apollo I episode of the all-too-openly-doubting Gus Grissom, Roger Chaffe and Ed White.
But we can consider one aspect that reliably exposes that Apollo was an absolute hoax. For that we can go to the astronauts' Portable Life Support Systems (PLSS), their space suits and attached backpack. Their design uses a pretty predictable, Earth-style air conditioning system. In the vacuum of space, however, there is no venting and recapturing of any heated-then-cooled liquid. There is no appreciable amount of cooler atmosphere or liquid available to radiate to and dissipate the heat buildup within the PLSS. The moon's atmosphere's moisture content is roughly comparable to Earth's at 190K'. Standing in 200-250F sunlight would make the astronauts pass out in a few minutes and see their blood boil in ten-fifteen minutes, killing them, of course. "Steam vent[ing]" as the PLSS manual depicts (attached picture) doesn't recapture cooler liquid in any return.
And by the way, there's no such thing as a negatively-charged particle, a so-called electron, as attested to by Nikola Tesla, James Clerk Maxwell, Oliver Heaviside, and C.P. Steinmetz. Einstein was a fraud (video), as Tesla maintained throughout his life. The particle physics fraud perpetrated on university physics departments gave the government the confidence that they could corrupt science departments as well with their alarmist Global Warming nonsense and then every other department with speech codes and Marxism.
University-based corruption has eviscerated the best minds from doing principled work. Bright, particularly conservative professors have long seen what they must do to keep their jobs and pensions if they wanted to sacrifice their integrities for them. PDJT sees this and backed out of the Paris Accord as a first step of reclaiming the universities. (PDJT's Uncle John Trump, an MIT professor, was charged with collecting and scouring Tesla's reportedly 47 trunks of papers and materials, much of which has never seen the light of public scrutiny.)
The Soviet program had several VAB transits including terrestrial lifeforms on the Zond 5 mission in Sept. of 1968. These included turtles, plants, and fruit fly eggs. The turtles experienced biological effects but it was determined that these resulted from diet deficiency and not the effect of spaceflight. The Soyuz 7K-L1 spacecraft and the Proton-K booster were in the process of being man-rated when the success of the manned Apollo 8 mission undercut political support for continuing the circumlunar efforts.
You said something about "equivalent" lead shielding and my point was that you don't necessarily need that depending on what you are shielding against. The VAB transit was of less concern than solar flares. For the solar flare issue, the big concern was coronal mass ejection. Particles from a CME event take some time to arrive, so the plan was to get the crew back into the CM, where the construction allowed for more shielding (about a 90% attenuation factor), and head for home to deal with any effects from acute radiation syndrome.
The picture you show is not the final version of the PLSS developed for Apollo by Hamilton Standard Division. You are showing an early design that was more applicable to Mercury and Gemini missions wherein the heat load was considerably less. HSD developed the final version of the lunar surface PLSS and required three new inventions. These were the liquid cooling garment, the multiple water connector, and, most importantly, the porous plate sublimator. You clearly do not understand how heat rejection works in an environment where convective cooling is unavailable. The porous sublimator plate takes advantage of the heat rejection that occurs with a phase change. That obviates the needed for a "cooler atmosphere or liquid" to effect heat rejection. HSD engineer John Lovell is credited with the idea of using the latent heat of vaporization in the heat rejection circuit of the PLSS. The design had a peak metabolic rate capacity of 2000 BTU/hr. The sublimated liquid is considered a consumable and that is why the PLSS has a specified use lifetime between recharges, which are done from the LM reserves following the EVAs. You also demonstrate a lack of understanding of the real problem with portable life support on the lunar surface. It is NOT heating from "sunlight". The insulation in the EVA suit was more than adequate protection for that, since the only effective heat transfer process on the surface is radiative heat transfer, which is quite inefficient compared to convection or conduction. The primary problem is internally-generated (metabolic) heat, and thus the need for the cooling garment and evaporative heat transfer.
No such thing as an electron, eh? OK, that does it, I'm done.