Regarding Cross and how it came to be: Masato Kato [who was one of the writers on Trigger] was the lead on a little visual novel from 1996 called Radical Dreamers [slapped together in about 3 months, incredibly]. Despite the compressed development, apparently Square pretty much let Kato write whatever he wanted for the game and that's what he did, eventually tying loosely into the storyline/world of Trigger [which even Kato admitted hadn't been his initial intent].
Fast forward a little bit, and it was Kato who led the Cross team, which was otherwise mostly people who hadn't been involved with Trigger's development [aside from Kato, the other major figure on the dev team was producer/designer Hiromichi Tanaka, who played a major role in the development of Secret of Mana 1 and 3, but wasn't involved with Trigger at all]. So, Kato, for whatever reason, decided to use the characters, world, and plot from Radical Dreamers as the main basis for Cross, rather than anything specifically from Trigger.
Trigger was basically Square's all-star team [3 directors: Takashi Tokita, Yoshinori Kitase, Akihiko Matsui; Kazuhiko Aoki producing; Hironobu Sakaguchi as main designer; Masato Kato as the main writer with input from Tokita and Kitase from an outline by Yuji Horii; and then toss in Akira Toriyama for good measure], while Cross was more the product of just Kato and Tanaka.