I wouldn't be opposed to an MCU-like approach with standalone movies for each monster before putting them all together again.
The monsters aren't the issue. There have always been recurring monsters and crossovers between them, but Toho kaiju movies have very rarely had any recurring
human characters. In the Showa series, Mothra's tiny twin heralds the Shobijin appeared in three films, but otherwise, there were at most two scientist characters who appeared in more than one film, Dr. Yamane from the first two films and Professor Miura from
Mothra vs. Godzilla and
Ghidorah, the Three-Headed Monster, although some sources report his character in the latter film as Professor Murai instead. There was even the weird case of
Frankenstein Conquers the World and its direct sequel
The War of the Gargantuas, in which the three lead roles were renamed, two of them were recast, and their backstory was retconned to a different city, even though it was explicitly presented as a continuation of the same storyline (except in the English dub where the Frankenstein connection is glossed over).
A couple of Showa characters were brought back in later films/continuities -- Emiko Yamane from the original film returned in
Godzilla vs. Destoroyah, and Chujo from
Mothra returned in
Tokyo SOS. But otherwise, the only recurring characters in the franchise were in the last six Heisei films (primarily the psychic Miki Saegusa, who was in all six films in roles ranging from supporting to lead) and in the two "Kiryu" films in the Millennium era -- plus the anime trilogy, of course, but that's just one long story in three parts, so it's not the same as a character returning in a later story.
The Heisei series was my favorite, largely because it's the only one with (relative) continuity and developing character and story arcs from film to film. For all that the Showa films crossed over and used each other's monsters, they otherwise had very little continuity and contradicted each other all the time. The Heisei films had their share of continuity conflicts, but there was an overall sense of interconnectedness, not just through the Miki character but through the way humanity's tactics for fighting kaiju advanced from film to film.
