I hate to answer my own questions, but I did finally find a solution that actually works (using socket communication between services may fix the problem, but it creates even more problems). Since our database is legacy, it merely required Microsoft.ACE.OLEDB.12.0
in the connection string. It turns out that this was also included in Office 2007 (and MSDE 2007), where there is only a 32-bit version available. So, instead of installing MSDE 2010 32-bit, we install MSDE 2007, and it works just fine. Other applications can then install 64-bit MSDE 2010 (or 64-bit Office 2010), and it does not conflict with our application.
Thus far, it appears this is an acceptable solution for all Windows OS environments.