Installing the dependencies of local modules without composer merge plugin

Currently I have a composer-based Drupal project with both third-party and custom modules. Third-party modules are managed by composer without any issues. But I would like my custom modules to declare their dependencies in a composer.json within their directories, and also have them install when I run composer install at the root of the project.

composer.json
web/
  modules/
    contrib/
      address/  
      admin_toolbar/
      ...
    custom/
      my_module/
        composer.json
        ...
      my_other_module/
        composer.json

Currently:

• I have the composer merge plugin which works fine for the most part but would like to avoid using it. It has a nasty habit of calling update and bumping dependency versions when it shouldn't.
• I've already looked into Composer path repositories. While it does install the dependencies of my custom modules, it also symlinks/copies my custom module into web/modules/contrib which is unnecessary because the custom modules are already in the right place in web/modules/custom.

In the future, I would splinter off these custom modules into their own projects and stored in their own repositories. But for now, they're still housed in the same project as the Drupal site I'm building.

How do I install dependencies declared in the composer.json of my local custom modules together with everything else?

This what I have to make it work:

web/modules/custom/my_custom/composer.json

{
    "name": "[provider]/my_custom",
    "type": "drupal-custom-module",
    "description": "My Custom Module.",
    "require": {
        "drupal/core": "^8.9 || ^9",
        "drupal/devel": "^2.1"
    },
    "minimum-stability": "dev",
    "repositories": [
        {
            "type": "composer",
            "url":  "https://packages.drupal.org/8"
        },
        {
            "type": "composer",
            "url": "https://asset-packagist.org"
        }
    ]
}

composer.json

{
...
  "repositories": [
    {
      "type": "path",
      "url": "web/modules/custom/my_custom"
    }
  ],
...
  "require": {
    ...
    "[provider]/my_custom": "*"
    ...
  },
  "extra": {
    "installer-paths": {
      ...
      "web/modules/custom/{$name}":   ["type:drupal-custom-module"],
      ...
    },
  }
...
}