fix(cdk-integ): Update cdk-integ to use new context file

[rix0rrr]

Running integ tests is currently broken, since the integ tests will
write context to cdk.json, which then gets moved to
cdk.context.json. cdk.json gets cleaned up afterwards but
cdk.context.json does not, so it gets left there and messes up the
next integ run.

Just write all fake context to cdk.context.json right now as intended.

---

Pull Request Checklist

• Testing
  • Unit test added (prefer not to modify an existing test, otherwise, it's probably a breaking change)
  • CLI change?: coordinate update of integration tests with team
  • cdk-init template change?: coordinated update of integration tests with team
• Docs
  • jsdocs: All public APIs documented
  • README: README and/or documentation topic updated
• Title and Description
  • Change type: title prefixed with fix, feat will appear in changelog
  • Title: use lower-case and doesn't end with a period
  • Breaking?: last paragraph: "BREAKING CHANGE: <describe what changed + link for details>"
  • Issues: Indicate issues fixed via: "Fixes #xxx" or "Closes #xxx"
• Sensitive Modules (requires 2 PR approvers)
  • IAM Policy Document (in @aws-cdk/aws-iam)
  • EC2 Security Groups and ACLs (in @aws-cdk/aws-ec2)
  • Grant APIs (only if not based on official documentation with a reference)

---

By submitting this pull request, I confirm that my contribution is made under the terms of the Apache-2.0 license.