First of all its great to communicate with a creative person, which I believe you are being a Writer. I would recommend using Wordpress as it provides the best solution for Blog sites. I have reviewed your description and the reference website minutely to have a clear understanding of your requirements.
We can certainly place a tool to Show the Articles categorically/month wise and provide an Advanced search and sorting panel on the right side for viewers to browse through the archives. The site will be linked to a MySQL database and we will provide you an user friendly Admin Panel to edit/update/delete and manage the contents of the site as per your will at any given point of time.
We would use latest Front-end development technologies like Node.JS, Angular.JS, HTML5, Bootstrap CSS etc. to craft a visually stunning yet professional design for your blog and make it responsive (mobile friendly), so that it opens perfectly on all devices and screen sizes, be it Desktop, Laptop, iOS and Android devices. The website would also support all major Browsers.
Kindly review some of our similar work on Wordpress:
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I'm associated with a 15 year old Software Development Organization based in Largo, Maryland, USA. We can commence work as per your convenience. I would request you to revert back to us, so that we can discuss further.