A dense editorial sentence with multiple embedded clauses. 尽力する ('to devote effort, to strive') is a formal verb for sustained effort. ~てきた marks a continuing past action extending to the present ('have been doing X up to now'). ~への is the composite particle 'to + attributive' — a common way to attach directional phrases to nouns. 黙らせる is the causative of 黙る ('to make silent'). 懸命になる 'to become desperate / frantic.' ~ようだ is evidential 'it seems that.'