Correct that an APN is difficult to challenge - there have been many cases in the Courts and aside from HMRC being told to follow their own rules, none have made much difference.
A GAAR pooling and counteraction notice can be challenged but not appealed. Usually HMRC will make amendments to assessments etc as part of the process and those can be appealed. If they arrive with an APN, you have to look to a different way of having the GAAR notices set aside.
That will begin with exchanges of views and will almost inevitably end in some form of litigation as Mr Reasonable packed his bags and left HMRC some time ago.