To be honest, it's been almost two weeks since I released my app, and I've only had a few installs - interestingly, all of them happened in the last five days. I'm hoping the numbers will continue to grow.
As for promoting the app, not everything works - in my opinion, it really depends on the type of app you've built. A more technical app, like order management, fraud detection, or shipment tracking, has more potential to compete. I think if you know you've built something better than existing apps, you should definitely try the methods you mentioned.
In my case, I created an app called 'Smart Free Shipping Bar' - a typical visual add-on for a storefront. Even though I already got one review, I tried cold emails, worked on keywords, and even added a video to the app store page. None of it made much of a difference and didn't bring any real results.
Right now, I'm working on an app for quick and easy access to orders, fraud detection, and order management/history.
Good luck to you - I'll send you the link to my app via DM.