Reintroduce working CI tests to GitHub Actions

[engn33r]

To continue the discussion from PR #309, the transition from TravisCI to GitHub Actions wasn't able to get the Makefile tests or Docker integration tests running properly. This could be from a lack of knowledge on my side, but there is probably an improved approach to these tests than what is in the older TravisCI flow. To move towards a fix, we should determine:

1. What did the Docker integration tests do?
2. What did the Makefile tests do?
3. What would be the best approach to getting the same results for these tests now that Go modules exist?