Nowadays, seems like that style has just been hardwired into KyoAni since the character designer for K-On! and Tamako Market, Horiguchi Yukiko, has already left the studio.
Going through a brief history of KyoAni's character designers:
DISCLAIMER: I'll be skipping the Munto movie series and the anime it spawned as it's pretty much the same deal as AIR in terms of staff. Also, many more people than those I'll be mentioning have formed part of the animation department of KyoAni, but I'll be focusing on those that got at any point in time credited as Character Designer or Chief Animation Director.
Their first big solo anime seems to be Full Metal Panic? Fumoffu (2003), inheriting the franchise from GONZO, bringing back the first season Character Designer and Animation Director Horiuchi Osamu. He'd reprise these roles for FMP Season 2 in 2005, but that's the last of him with KyoAni. He's just here for historic reference, I don't think he had that much influence in the KyoAni style.
In between the FMP seasons, they made AIR (2005), an adaptation of a KEY Visual Novel (get used to this), by the hand of Character Designer and Chief Animation Director Aratani Tomoe. Of note here are Ikeda Kazumi and Ikeda Shoko taking over as Animation Directors for certain episodes; and also being Key Animators alongside Nishiya Futoshi and Horiguchi Yukiko. You could call this the early stage of KyoAni's style.
In comes 2006 with The Melancholy of Suzumiya Haruhi, now with Ikeda Shoko as Character Designer and Animation Director. This time, Nishiya and Horiguchi got to direct some episodes themselves along Aratani and Ikeda Kazumi, they all worked in Key Animation as well.
Later that year, they all worked on Kanon (2006), a new adaptation of yet another Key VN, this time with Ikeda Kazumi as Character Designer and Chief Animation Director (CAD). The rest of the team mentioned earlier also worked as individual episodes Animation Directors and on Key Animation.
Spring 2007 brings us our star. Horiguchi Yukiko gets to be Character Designer and CAD for Lucky Star. Same as before, we get all our familiar faces working on Animation Direction or Key Animation, with a new addition: Kadowaki Miku on Key Animation. Lucky Star (and the first season of Haruhi to some extent) seems to me to be the middle point between the KEY adaptation style and the later KyoAni style, I believe working on this, adapting the 4-koma chibi style of the manga, helped cement Horiguchi's style for later works.
Later that year, Ikeda Kazumi is back helming Clannad, again with a KEY adaptation. The regular team is at it again, but this is the second to last work with KyoAni for Aratani, and since her last work was the finale for the Munto series which I said I won't be expanding upon, this is the last we'll see of her in this overview. I believe she had an important role in nurturing the talents in KyoAni through her work in AIR and Munto. Clannad After Story in 2008 continued with the same staff sans Aratani and is to this day the most beautifully crafted of any KEY VN adaptation ever made.
2009 was a big year for KyoAni. First with 2 Haruhi ONA series with Nishiya at the helm, followed by K-On! with designs by Horiguchi Yukiko (and Kadowaki gets a role as Assistant Animation Director for ep 12) with her style now in its full glory, and Haruhi Season 2 with Ikeda back as Character Designer but with Nishiya as CAD (and Kadowaki as a full-on Animation Director herself for episodes 7 and 13). This is the year that pretty much set in stone the artstyle that you're looking for. It can be clearly seen how Horiguchi's style had permeated into the rest of the team with Haruhi S2, where you could see in some episodes more similarities between it and K-On! than with the first season, same deal with the Disappearance of Haruhi Suzumiya movie in 2010 (Also, K-On! S2 also aired on 2010).
In 2011, Nishiya is back as Character Designer and CAD for Nichijou, and then back to Horiguchi with the K-On! Movie. The Ikeda siblings seemingly left temporarily, as they had no participation in the K-On! Movie.
Now, it's 2012, we start with Hyouka, with Nishiya back at the head, with a more... let's say elegant (?) style, while still resembling Horiguchi's, this is what will become what I like to call late KyoAni style. Later that year, Ikeda Kazumi is back leading Chuu2Koi, and here is where you can see how much of an impact Horiguchi had made. Despite her not having any role as Key Animator, nor directing animation in any episodes, you can clearly see that her style from K-On! is all over the place.
Horiguchi is finally back in 2013 with Tamako Market, her last TV anime with KyoAni. That same year, Free (Nishiya) and Kyoukai no Kanata (Kadowaki's debut as Character Designer and CAD, and also Takase Akiko joined as Key Animator) further develop the late KyoAni style into what we see nowadays. Chuu2Koi S2 brings back the softer style even without Horiguchi, and the last we see of this pure Horiguchi style from KyoAni will be 2014's Tamako Love Story.
After her leaving KyoAni, seems like she's been working on the mixed media idol project "22/7" which had an anime last year (the idol project seems to have started on 2016 tho), and the Graphinica movie "Hello World" from 2019. She was also the illustrator for the Kokoro Connect light novels. Those would be closest chances if you want more of her undiluted style.
KyoAni on the other hand went on to develop its style with Amagi Brilliant Park in 2014 (Kadowaki). The Ikeda siblings seem to be the ones that were most influenced by Horiguchi, Hibike! Euphonium in 2015 (Ikeda Shoko's comeback) and Musaigen Phantom World in 2016 (Ikeda Kazumi) have a much closer style to Tamako Market than other later works of KyoAni. But Nishiya clears the way to the late style with 2016's masterpiece Koe no Katachi and culminating with Takase Akiko's debut as Character Designer in 2018's Violet Evergarden (in between these 2 it was mostly sequels and spin-offs from Free and Euphonium).
What was the point of this overly long explanation instead of just saying "Horiguchi Yukiko"? Because I believe that the style in KyoAni's work is not simply one person's work. Even though the biggest influence comes from Horiguchi Yukiko, the current state of the style was made possible through KyoAni's own work ethos and a lot of work from Nishiya and Kadowaki who developed the style after Horiguchi's departure. Them alternating character designers and animation directors helped nurture new talent and create a style of their own that wasn't just a single person's but the studio's as a whole.
And about the arson incident, unfortunately it took the live of Nishiya Futoshi, may he rest in peace.
