Here's the problem you're going to run in to: technically speaking, no high-definition from the 68 special is capable of existing due to the medium used for production.
The Singer Presents Elvis TV Special was recorded on videotape, not film whereas The Beatles: Get Back was filmed on 16mm stock. Unlike Get Back, which could be blown up and digitally restored, there's just a non-negotiable upper limit of quality that's able to be pulled out of those tapes.
The Blu-Ray set that's available through Graceland was a restoration overseen by Thom Zimny, the director of Elvis Presley: The Searcher and presents the least compressed version of those tapes. Disregard the one review you found - that person is wearing rose-colored glasses - the footage on the Blu-Rays are as good as technologically possible given the source and way, way superior to VHS, VCD or DVD due to less compression.
"But users on YouTube have it in HD!" I can hear some other people saying.
The official YouTube channel uses better quality than any fan has in their possession and still has artifacts inherent to the videotape used in 1968, like pretty heavy motion blur and chromatic aberration that have caused restoration attempts to look bad.
"But 4K AI Upscaling!" I hear.
The vast majority of fan attempts at restoration, which almost always feature heavy noise reduction as well, have ended with smeary results that actually remove the few fine details we have. Take a look at Elvis's hair on this "restoration": https://www.youtube.com/watch?v=Q0EPSm_d2Pc
Versus the (compressed YouTube 1080p) version of the original tape, where, although it is a little blurry, still retains a lot of detail and individual locks of his hair are pretty noticeable: https://www.youtube.com/watch?v=WVxL1e7ZGLw
It's been a vocal minority but there are fans who were critical of Peter Jackson's heavy use of noise reduction as well, and a number of shots in Get Back DO have a slightly muddy/painted look due to the blurring. But I think it's easier to let slide there because the overall quality of source material has a higher ceiling than the 1968 tapes do, just as 35mm stock, 70mm stock or 4k/8k HDR footage has a higher limit than 16mm. In fact, there's a discussion in Get Back where The Beatles & the director talk about wishing they'd gone with 35mm to begin with if they'd known it was going to be a movie, but that it should scale up well.
It's why the official Paramount 4k restoration of King Creole (and subsequent 4k-sourced 1080p downscaling on Blu-Ray) looks SO damn crisp, despite being shot 10 years earlier than the Singer Special, it was made on 35mm, as were all of Elvis's feature films: https://www.amazon.com/King-Creole-UHD-Elvis-Presley/dp/B0845VYZN2/ref=sr_1_1?keywords=king+creole+4k&qid=1638930271&sr=8-1