(Tokyo Puck cover, 1905, from Birth of a Million Seller, used for review purposes only.)
It's important to note here that some of the illustrators listed by Gekkan Bijutsu didn't explore manga or panel strips to much of an extent, if at all; Katsudi, Takeo Takei and Yumeji Takehisa being the main exceptions. But, the influence of the cover artists and story illustrators on the rest of the magazines is pretty inescapable, since many of these people made it into editorial positions at some point. Further, with the ending of WW II and the appearance of Tezuka's "Shin Takarajima", shojo magazines proceeded to be the main monthly stage for manga as we currently know it, for about a decade.
(Tokyo Puck inside page, 1905, from Birth of a Million Seller, used for review purposes only.)
Granted, panel art didn't just appear in shojo magazines. Newspapers had western-style comic strip sections, and many of the artists also illustrated the serialized novels running in the papers. But, the important point here is that these early artists tended to come from different backgrounds, such as avant-garde art circles, postcard printing, fashion and newspaper editorials. They then go through a convergence that takes them either through shojo magazines on to children's book publishing, or to editorial strips, and this convergence set the tone and pace for the manga leading up to 1947. I admit that I may be off the mark here, so feel free to correct me if necessary.
(Rakuten comic, from the wiki article, used for review purposes only. Compare the character designs to Winsor McCay's "Dreams of a Rarebit Fiend" series, which started in 1904.)
Switching paths, we backtrack to the turn of the Twentieth Century, and the advent of Rakuten Kitazawa (1876-1955). Born Yasuji Kitazawa, he took on "Rakuten" as a pen name. From the wiki page, "he studied western-style painting under Ohno Yukihiko and Nihonga under Inoue Shunzui"; in 1895 he started working for the English language magazine Box of Curios and learned how to draw western cartoons from Australian Frank Arthur Nankivell. (Frank would later go to America to work at Puck magazine).
(Frank Nankivell picture from Puck magazine. From the wiki article, used for review purposes only.)
In 1899, Rakuten started working at the daily newspaper Jiji Shimpo, founded by Yukichi Fukuzawa, in the Sunday comics section Jiji Manga. He started up Tokyo Puck in 1905, a satirical full-color magazine, and Rakuten Puck in 1912. He returned to Jiji Shimpo in 1915 and then finally retired in 1932. While Rakuten popularized the word "manga", according to the wiki entry his predecessor at Jiji Shimpo, Ippyo Imaizumi is probably the one to first start using it "in the narrower sense of 'caricature'". Most sources credit Rakuten for using "manga" in the 'caricature' sense, moving it way from its original reference to ukiyo-e woodblock prints.
(Ippeo Okamoto picture from Lambiek.net, used for review purposes only.)
Tezuka is reported to have claimed Rakuten and Ippei Okamoto (岡本一平) (1886-1948) as his two main influences. Ippei, according to the Lambiek.net page, worked as a political cartoonist for Asahi Shimbun starting in 1912. He also produced comics for various magazines, starting with "Kuma o Tazunete". In 1921, he went globetrotting and when he returned to Japan he introduced American comics like "Mutt and Jeff" and "Bringing up Father" to Japanese audiences through the Asahi Shimbun. He produced his own artwork as well, including caricatures and advertising illustrations. He also wrote at least one novel.
The problem with treating Rakuten and Okamoto as "manga artists" (in the way I'm approaching it) is that for the most part they were either doing political cartoons, or Japanized versions of western strips. "Localized" yonkoma and panel strips as what we expect to see as "modern manga" (post-Tezuka) appear more with Katsudi and Suiho Tagawa ("Norakuro") in towards the late 1920's.