I, personally, would just place PDF pages into a new InDesign document. Set the "facing pages" as a larger page in InDesign and position each half.
Many may not realize that it's possible to have different size pages in a single InDesign file.
In InDesign, if you grab the Page Tool you can then highlight a page in the Pages Panel, and change its dimensions in the Control Bar across the top of the screen. This will change the highlighted page and not the entire document. (You have to have the Page Tool active in the Toolbar.)
Then merely place your PDF pages into this new document (similar to placing images), position correctly, and then export to a single pages PDF. While some pages are the size of a spread in InDesign, they will be "seen" as a single page in the PDf.
This would give you want you want with minimal effort.
Note you can "place" InDesign pages from one INDD document into another InDesign document. You don't necessarily need to have a PDF of any InDesign document to do this.
I don't think it's possible to use more than a single option for page display in Acrobat. I could be incorrect though.