I'm unsure by what we even mean by "mainly" or "mostly" right- or left-branching in a comparative context. I mean, sure, I can see how Japanese is mainly left-branching; but if by "left-branching" we mean OV + postpositions, and "right-branching" is VO + prepositions, then WALS would like to remind us that some languages have OV + prepositions (including Persian, Kurdish, Tuvaluan and at least 13 known others); and some languages have VO + postpositions (including Guaraní, Finnish and 40 others).
So all combinations of adposition and verbal argument order occur, although some are rarer than others. We could compare the two directionality variables (verb-object order, and adposition order) with an "agglutinative" parameter. But "agglutinative" is a category that mixes up several different things, and (to my knowledge) there's no easy way to define it in WALS. I tried to approximate it as a combination of exclusively concatenative, case, and time-aspect-mood monoexponential. Under this definition, this map allows you to compare the parameters in all possible combinations.
In particular, the following languages are listed as VO, prepositioned, and basically "agglutinative" (concatenative, monoexponential case and TAM): Squamish, Malagasy. The following have prepositions, VO, no morphological case, and may be more or less "agglutinative" depending on how you define it—it ends up including English!: Warembori, Hatam, Abipón, Cayuvava, Arapesh (Mountain), Luvale, Maung, Mixtec (Chalcatongo), Jakaltek, Zulu, Swahili, and English.