Debugging a test shouldn't be hard. Use inspect-process to easily launch a debugging session with Chrome DevTools.
$ npm install inspect-process -g
Modify package.json so your scripts -> ava entry will look like this:
"ava": "TEST_ENVIRONMENT=true inspect node_modules/ava/profile.js --concurrency=5 --verbose --timeout=1000s --require babel-register",
(cross-env removed above, inspect command is used, we run /ava/profile.js, output set to verbose, timeout to 1000 seconds).
Set breakpoint(s) in your test(s), just use debugger; keyword inside the test.
Run the test with npm run ava ./file/to/test.js