You could maybe duplicate your 7-page PDF, open up the first, and then use the "Create PDF" tool with "Multiple Files" and "Combine" your first PDF with the duplicated second. That'd get you a 14 page PDF. Repeat the process over and over until you are finally combining a 350-page PDF with another 350-page PDF. Might be faster than copy-pasting a bunch of times.
There's such an easy way to do this in native Acrobat. Takes only a few minutes.
With thumbnails showing, select all 7 pages, hold down the Ctrl key, and drag the cursor to after the last page. Now you will have 14 pages (1 thru 7 and 1 thru 7). Repeat with all 14 pages to make 28, repeat with 28 to make 56, 112, 224, and so on. If you create more than 700 pages, delete them.
To make life easy doing this, drag the thumbnail pane wider so that you have 7 pages per row.