The Western Church tradition has never overly relied on 1 Tim. 3:16 as a proof-text for the Trinity. In fact, the Catholic NAB reads: "who was manifested in the flesh, vindicated in the spirit, seen by angels, proclaimed to the Gentiles, believed in throughout the world, taken up in glory."
Footnote from NAB on 1 Tim. 3:16: "Who: the reference is to Christ, who is himself 'the mystery of our devotion.' Some predominantly Western manuscripts read 'which,' harmonizing the gender of the pronoun with that of the Greek word for mystery; many later (eighth/ninth century on), predominantly Byzantine manuscripts read 'God,' possibly for theological reasons.
Here is how the Douay-Rheims and Vulgate handle the passage:
"And evidently great is the mystery of godliness, which was manifested in the flesh, was justified in the spirit, appeared unto angels, hath been preached unto the Gentiles, is believed in the world, is taken up in glory" (DR).
"Et manifeste magnum est pietatis sacramentum, quod manifestatum est in carne, justificatum est in spiritu, apparuit angelis, praedicatum est gentibus, creditum est in mundo, assumptum est in gloria" (Vg).
Gordon D. Fee reports: "This reading ["God"] came to predominate in the Greek church (never in the West, since the translation into Latin happened before the variant arose)."
See his NIB Commentary on the Pastoral Epistles, Page 95.
NET Bible: "He was revealed in the flesh, vindicated by the Spirit, seen by angels, proclaimed among Gentiles, believed on in the world, taken up in glory."
See the long note (24) in NET Bible here: https://net.bible.org/#!bible/1+Timothy+3