Frank Kogan

Apparently, The Runnaways were more famous in Japan than they were in the States, so it may be the case with other artists having some unknown momentum overseas. But you're right, it does seem an odd choice for a psychedelic band to cover, much less in the direction they arranged it with.

The information section on the "Magic Colors" names some fellow bands from the era. I don't have enough knowledge to know if the songs I sampled from the list were adventurous the way you're characterizing current Kpop, and it all fell under "60s sounds" to my ears, but bands did seem to cover whatever sounded cool, and not necessarily trying to adhere to one particular genre. The Mystics sounded less British Invasion and more crooner, though. Of course, these bands were mainstream popular in Hong Kong at the time, and may not count as hipsters, other than in their defiance of the government's condemnation of Western music.

LLO: Remee, Troelsen, Lucas Secon, and Yong-Hun Cho
Juliette: Remee, Mich Hansen, Joe Belmaati, and Jay Sean
Sherlock: Troelsen, Rocky Morris, Thomas Eriksen, Rufio Sandilands, lyrics Jo Yoonkyung
Remee and Troelsen seem to be pretty able to replicate each other's sound, so Troelsen was probably following the precedent Remee had set for Shinee.
With a side-by-side comparison, I'd say the arrangement also played a role in how much better "Juliette" sounds. "Deal With It" is sparse and thus requires more of its performer, which Corbin doesn't quite deliver. "Juliette" not only has more members to cover for that, but the arrangement has its own heft as well, allowing Shinee to sing in more of a whisper-y style, doing a charming laid-back serenade instead of the forceful angry rant of "Deal With It." The arrangement for "Juliette's" bridge even has some little disco touches for extra glitz and glamor.
But the main melody of both songs could work for a soloist given a Guetta-style arrangement with electro squiggles. Including the Shinee vocal adlibs, it has Enrique Iglesias written all over it.

My first instinct for Jpop is 50s-70s, where Kpop tends not to go further back than 80s, (unless mining for disco) but the longer I think about classic Jpop bubblegum the murkier possible composition influences get, other than the fact that some of it definitely developed as if the 80s/90s/00s never happened.