Your fix would be best.
I was looking into a quick fix with as little drama as possible. Trim pieces and my clumsy use of trim tools usually results in broken tabs and the resultant cussing.
A solid Belville conical spring washer or three, used as shims, would likely tighten up the gap. Of course, once you tear into the project, you would be down a mirror until you sourced the correct washer/shim. Possible items:
Source for spring washers and
Shims
I chose the easy button.
Question: where and how are you accessing the Toyota shop manual instruction and such; Toyota service manual subscription perhaps?