Transparency and overprinting are two completely different things. Transparency effects involve blending the color values of an object and the objects underneath using one of a handful of formulas (multiply, screen, normal, difference, etc.) with an opacity variable, or using an alpha channel image. Overprinting objects are essentially opaque, but only affect the colorants that they contain, leaving the other colorants the same as they would be if the object were not there (e.g., 0/0/0/100 CMYK set to overprint leaves CMY unaffected, but 1/1/1/100 CMYK completely knocks out all CMY underneath). I think transparency effects should appear accurately going back to probably Reader 5 without having to change any default settings. I think overprinting preview may be on by default since reader 8 or 9, but maybe that's only for /X-1a.
The discrepancy between what the customer sees and what you will print is more of a problem when they don't realize anything is different. For example, if there is overprinting text that is white or some color other than black that they don't really want to overprint, or a black image set to overprint a spot color underneath that shouldn't - in these cases what they will see looks fine, whereas what you will print does not.
You might try printing to the printer "Adobe PDF..." from Acrobat to generate a new PDF, and use the "simulate overprint" option. If, for example, you have 0/0/0/50 CMYK text set to overprint 100/0/0/0, it will render the text as 100/0/0/50, changing the color of objects to achieve the same result as overprinting. I think Adobe may have included this for printing to desktop printers that normally ignore the overprinting attribute. If you want to give the customer the same PDF you are putting in the RIP and not a post-processsed one, and you are making the final PDF from Indesign, it also has the same option, but you won't be able to preserve transparency when you "print" instead of export.
Another possible workaround may be to change objects that overprint to knockout and change the blending mode to multiply, but that's certainly a time-consuming kludge, and would not yield identical results in many cases.
We use an Apogee RIP and Printdrive to store and manage the raster images and make proofs and plates from those images. I always make PDF proofs from there, because it is much safer than sending an abstract pre-RIP PDF, and every PDF page is a single flat CMYK image with spots converted to process - can't get much safer than that. Printdrive stores separate resources for each page because we use DQS (digital quick strip), so it can make a PDF page for every document page instead of an entire flat.