The JSC does have the cloudy shot. Every NTSC transfer prior to 1993 did. The ONLY official transfer pre-THX I know to have the cloudless version was the 1989 French widescreen LD transfer. And that version DID have the burns.
The cloudy Yavin was not added with the credits fix. It could actually be the opposite - setting aside the official releases, every privately-owned print or bootleg tape I know of with the original end credit roll has the "cloudy" composite (your VHS, the "Moth3r" telecine, Puggo Grande), while the ones with the revised credit roll always have the cloudless version (the Spanish LPP print, the Treadwell/Starkiller/MeBeJedi full-frame bootleg, and possibly the British IB prints). I think the PuggoKrig Swedish 16mm print has the revised end credits - can someone check and see if it has the cloudless Yavin shot?
I think I said this before, but the reason the R2/3PO shot was "redone" for the SE was because the original violent shake was an optical effect similar to the ones right before the TIE battle. The operator did shake the camera on-set, but the end result was obviously judged to lack the necessary impact, so each frame was optically repositioned and smeared to give it that extra oomph.
During the SE restoration, that optical was either deemed to be too grainy due to the generation loss, or couldn't be used because the CRI stock had deteriorated. So they went back to the original camera negative - which only had the on-set camera shake.
The TOE-less transfers have the same optical shake, just not the burns.
And for the record, Ben Burtt said there was a jumpy spot when the Stormtroopers burst through the door - we on the forum were the ones who theorized that he was referring to the orange burn marks.
He also said that he damaged the color work print, and that at the time it was the only work print of the film. He wouldn't have been running the negative through a moviola. And the workprint would have been made from the negative, not vice-versa, so if Burtt damaged the workprint, it wouldn't affect the negative. He only said that "all the screenings from then on always had this jumpy spot right when the stormtroopers come bursting through the door of the Blockade Runner." He didn't clarify if that meant all screenings of that one workprint, or all screenings of the film, period. (We don't even know if this workprint contained the optically manipulated version of the scene, or the original production footage as seen in the SE.)
This is all very confusing because the literature at the time of the THX transfer said that Fox/LFL had to hunt down first-generation IPs because all the ones they had access to had subtitles:
"One small difference from the original films is that in letterbox transfers we prefer to put any subtitles in the black border beneath the actual picture area. Thus we didn't use the same interpositive as the theatrical one, because that one contains subtitling already. In tracking down the elements, we found that the only ones in the vault were ones with subtitles- these clearly weren't the first generation off the camera neg because they had to have the subtitles burned in. So a massive search was undertaken and the first generation IP's were found in a special vault having only opticals in Los Angeles."
But they already had access to subtitle-free IPs when they made the previous letterbox transfers in the 80s, and they are clearly not the same IPs that were transferred in 1993. The IP used in the old transfer had no TOE's and the cloudy composite - the IP used in the new transfer had the TOE's and the cloudless composite. I'm stumped...