The funny thing about trunkver being "compatible" with semver is that it is not semantically compatible, only format compatible.
You could (but not necessarily should) combine them by making the trunkver the "patch" part of semver.
In our work, the semver is kept separate from the build version. We use a build versioning of vYYYY-MM-DD[.hhh] where hhh is for a "hotfix" of a previously released version.
The version of the "next" release can be set (either in advance, or based on a sprint or just the current date).