Laravel 7.4 - Outside of regular expressions, is there any way to validate the parameters of the URL string in a GET request?

Question

I have a URL of the following form:

GET /cat/{cat}/meows/{overTime}

I can write a controller method that looks like this in order to capture the values:

public function getMeowsOverTime(Cat cat, int overTime)

What I would like is to validate the {cat} and {overTime} values before it gets to the controller method.

I have tried creating a custom MeowsOverTimeRequest object that extends Illuminate\Http\Request according to the recommendation here: Laravel 5.7 - Override all() method in Request validation Class to validate route parameters?

So that would be:

class MeowsOverTimeRequest extends Request
{
    public function authorize()
    {
        return true;
    }

    public function all($keys = null)
    {
        $request = parent::all($keys);
        $request['cat'] = $this->route('cat');
        $request['overTime'] = $this->route('overTime');
        return $request;
    }

    /**
    * Get the validation rules that apply to the request.
    *
    * @return array
    */
    public function rules()
    {
        return [
            'cat' =>
            [
                'required',
                'integer'
            ],
            'overTime' =>
            [
                'required',
                'integer',
                Rule::in(Cat::getMeowTimeOptions())
            ]
        ];
    }
}

But $this->route('cat') and $this->route('overTime') both return null. How can I access these variables?

I would prefer not to use regular expression validation due to the overTime being limited by what is returned from Cat::getMeowTimeOptions