Hi! I'm a solo web developer from Europe, Serbia.
I have checked the attached file and I can implement all of these features. I haven't worked with [login to view URL] API, but I worked with other JSON APIs.
I can use a PHP micro framework which is not bloated like Laravel and others. I personally recommend Silex (an excellent framework from the creators of Symphony) or Slim PHP.
I can also use PHP-CLI to create a scanner which will be started by a cron job or will run always in the background and will fetch the new data from Archive.org.
To be honest, I'm mostly a back-end dev, my design skills aren't the best, but I can code the front-end too if you provide an image or Photoshop layout that I can follow (You mentioned you would hire a designer. Designers only design, but front-end developers create a HTML/CSS code for it).
I can start tomorrow morning (I'm in the Central European Timezone), and I would like to discuss the milestones with you before I start any work.
Feel free to contact me.
Regards,
Ákos