Not sure I am understanding the issues here TBH.
If you are the only user having address lookup issues and sync issues, how would making the BESAdmin account a Domain Admin help with that?
TBH, RIM says do NOT put BES Admin as Domain Admin, it will cause problems.
So if you're having a side issue that you thought this might fix, please feel free to post the full issue and we will see if we can work it out. Either way, a good fix is not BESAdmin=Domain Admin