Hi Brenker,
What you are referring above is achievable, without using the Document Cloud web service. Saving a pdf into other file format is a process of Exporting pdf.
We see that you are entitled to Acrobat DC and Export service. These services works on web as well as using desktop application Acrobat DC and Adobe Reader DC.
1-Using Export PDF you can use free desktop application Adobe Reader DC you can open a pdf into Reader and using Export PDF tool it can be exported to other format. Open PDF>Export PDF

2- Using Acrobat DC you can follow the same steps, or simply File>Save As>choose the format for saving PDF.
Note: Export PDF service only helps you exporting file to different format. And what you were looking for (File>Save As) is only available with Acrobat DC subscription.
Hope this answers your query.
Regards,
Akanchha