Typically I understand that the plan adminsitrator picks the TPA, but that sometimes is bundled with the investment funds. Shouldn't trustees be the ones ultimately signing off on the investment fund arrangement or am I overthinking things?

The specific question is who needs to actually sign off on a change in the investment arrangement, the plan administrator or trustees?

The document has pretty "typical" language about trustees being responsible for investments.

Has always been my experience that the ER/plans sponsor names Trustee. That could be themselves or someone else. But whoever it is is a fiduciary of the plan and now responsible for selecting and monitoring the funds offered by the plan. Make sure the ER understands that they can delegate the responsibility but are required to monitor those they delegate to.