IMHO, I'm not even sure that going back to KH's original writing team would fix the mess that KH is in these days. Back when KH1 was first released, Nomura didn't have as much "power" over the series to do whatever he wanted--he was the character designer who created the physical appearances of the characters. The writers worked to craft the plot with the characters Nomura offered them, and Executive Producer Shinji Hashimoto oversaw the production of it all. Nomura couldn't go wild creating and introducing new characters into the story as he pleased because he required someone else's approval to do so. Similarly, the writers couldn't get too ridiculous with the plot twists and shove them into the story whenever they wanted. Not without Shinji Hashimoto's approval, of course. And the fact that the original KH1 is still regarded as a "magical" experience shows how well Hashimoto succeeded in keeping everyone's whims in check and kept them focused on their tasks.
Hashimoto served as KH's original Executive Producer until BBS, after the release of which he retired from the position and left Nomura to take his place. And I think we can all agree that it's post-BBS, after Hashimoto retired and Nomura took over control of the series, that things got out of hand and KH's plot truly began to get crazy with things like time travel, body surfing, random plot twists, etc. The fact that Nomura went straight from character designer to executive producer of the KH series meant he could do whatever he wanted, no questions asked.
And, IMHO, I think that's what's really wrong with the series these days. Nomura has too much power to just do whatever he wants with it. KH1's plot had some awkwardness, but it was definitely easier to understand than what Nomura's now writing post-BBS. What's the saying? "Power corrupts and absolute power corrupts absolutely." In KH3, Nomura gave himself not just one or two jobs to work on, but THREE: Executive Producer, co-writer, and character designer. That's A LOT of influence for just one person to have in the development of a SINGLE GAME.
So can the KH series recapture the ‘magical’ feeling of the original KH1 game? IMHO, that's a blunt no. I think a more appropriate question is whether or not Nomura can improve his writing skills to match the feeling of the original KH game.
(Also if I got the name wrong of KH1's executive producer, please let me know and I will edit the post to change it!)
ETA: Just making things more readable. My initial post was a mess. lol