Applying to a "Big Three" Bachelor's with a DEAC Master's degree

[openair]

In the not-so-distant future, I am planning to apply to one of the "Big Three" Bachelor's degree programs in Liberal Arts. I reside in Europe. Here's my question: Are there any advantages to applying to one of these Bachelor's programs with a (soon to be achieved) Master's degree from a nationally accredited (DEAC) institution? Would I actually be better off applying with my foreign Bachelor's degree after a U.S. evaluation that provides a regional degree equivalency? Does the fact that you hold any of these prior degrees provide any type of advantages in terms of reducing the general requirements for the Bachelor's/capstone exemptions, etc? I don't mean the individual course transfers, but the general work that must be done to obtain the degree, if this isn't your first degree. Lastly, are you obliged to present all your prior degrees upon admission, or just your highest achieved degree?