Create react app template module not found when creating from custom template

I am trying to create a custom cra-template file for my team to use, but keep hitting an issue where I receive the following error when running npx create-react-app test-app --template my-custom-template.

internal/modules/cjs/loader.js:796
    throw err;
    ^

Error: Cannot find module 'cra-template-my-custom-template'
Require stack:
- C:\Users\user\Desktop\cra-test-app\test-app\node_modules\react-scripts\scripts\init.js
- C:\Users\user\Desktop\cra-test-app\test-app\[eval]
    at Function.Module._resolveFilename (internal/modules/cjs/loader.js:793:17)
    at Function.resolve (internal/modules/cjs/helpers.js:80:19)
    at module.exports (C:\Users\user\Desktop\cra-test-app\test-app\node_modules\react-scripts\scripts\init.js:110:13)
    at [eval]:3:14
    at Script.runInThisContext (vm.js:116:20)
    at Object.runInThisContext (vm.js:306:38)
    at Object.<anonymous> ([eval]-wrapper:9:26)
    at Module._compile (internal/modules/cjs/loader.js:955:30)
    at evalScript (internal/process/execution.js:80:25)
    at internal/main/eval_string.js:23:3 {
  code: 'MODULE_NOT_FOUND',
  requireStack: [
    'C:\\Users\\user\\Desktop\\cra-test-app\\test-app\\node_modules\\react-scripts\\scripts\\init.js',
    'C:\\Users\\user\\Desktop\\cra-test-app\\test-app\\[eval]'
  ]
}

The template itself is fairly simple at the moment and I think the issue here may be that our team uses a private feed for some internal packages (which are dependencies in the template). This private feed is set to use npm as an upstream feed.

I have tried testing the template locally with the --template file:../path/to/template method and publishing the template to our internal feed. I can install the package using npm install, so the package is definitely being found in the registry.

I have also tried refreshing the npm cache and uninstalling create-react-app per some other recommendations.

Do I have to publish the template to the public npm registry for this to work? Or am I missing something else?

My template's package.json file is as follows:

{
  "name": "cra-template-my-custom-template",
  "version": "1.0.5",
  "keywords": [
    "react",
    "create-react-app",
    "template",
    "typescript"
  ],
  "description": "The base template for React apps hosted within our project",
  "files": [
    "template",
    "template.json"
  ]
}

and the template.json is as follows:

{
    "package": {
      "dependencies": {
        "@<custom-feed-scope>/<custom-feed-library>": "^5.11.0",
        "@testing-library/jest-dom": "^4.2.4",
        "@testing-library/react": "^9.5.0",
        "@testing-library/user-event": "^7.2.1",
        "@types/jest": "^24.9.1",
        "@types/node": "^12.12.34",
        "@types/react": "^16.9.32",
        "@types/react-dom": "^16.9.6",
        "<custom-feed-library>": "^3.2.1",
        "<custom-feed-library>": "^0.2.4",
        "typescript": "^3.7.5"
      }
    }
  }

I am currently using npm instead of yarn, but I was able to create an app using the typescript template just fine.