How are we spent the 5/10-minute build time?
2-7 minutes for building/pulling/caching your containerized image (pre build your image, CI build just pull the cached image / update the cached image if necessary). 2 minute seems like the case when you cached your image right.
Break down each of your suite/linting/business checks to roughly 3-minute piece and running them in parallel after image built/pulled.
To achieve this, try Buildkite.