We use gitlab at my place, though we’re considering a transition to Seed.
Not sure your plan will work. Self-hosted build agents usually need to have a persistent connection to the build management system, and I’m fairly sure this is the case for GitLab too.
In general if your build needs are fairly simple my advice would be to use someone else’s hosted build containers and just pay for the build minutes. Overall tends to be cheaper than running your own infrastructure and maintaining your own build images.