Printing reader's spreads from a PDF of single pages

I am a professional in the design field and have used InDesign and Acrobat for years but cannot find the answer to this problem.  My hunch from searching many forums is that there isn't a solution, but it's such a simple and common functionality I find that hard to believe, so looking for the official Adobe answer to this.

I have a book created in Indesign. My printer wants single page PDFs. No prob. However, before I release the job I need to proofread it and check everything. In Acrobat the file is set to two-page view, with "show gaps between pages" unchecked. So the file views properly as reader's spreads with no space between the two pages on each spread. It also shows the cover as a single page as it should. The question is how do I print the file to appear this way? In my print settings I have it set to print 2x1 in the multiple pages section, but I cannot find any setting to make the pages butt together. I also have to print page 1 separately to have the cover print as a single page. Sure, I can rip a pdf as spreads from InDesign, but this is a huge file, takes a lot of time, and I need to print files like these often. This is not a complicated printer's imposition task requiring 3rd-party software as I've seen mentioned elsewhere as a possible explanation*. I just want to print spreads like I do from InDesign. What am I missing here? This seems like it should be a very simple task, as it is in InDesign.

* And by the way, Acrobat has a Print Booklet setting, but it also has this problem (will not print two pages side-by-side without space between them). I would expect if you offer a Print Booklet setting, it would actually print a booklet properly. It's really aggravating, because my InDesign files are huge and take forever to print as booklets directly from the indd file.