Just came up with another ay to phrase the inherent ability score increases...
Think of an inherent ability score increase as an instantaneous effect (since it cannot be dispelled and I cannot find any other magic that cannot be dispelled that is NOT instantaneous).
Now, IF it is an instantaneous effect and this is what makes it an INHERENT bonus we must take a look at what Inherent means?
Inherent -
http://www.m-w.com/cgi-bin/dictionary
Main Entry: in·her·ent
Pronunciation: -&nt
Function: adjective
Etymology: Latin inhaerent-, inhaerens, present participle of inhaerEre
Date: 1581
: involved in the constitution or essential character of something : belonging by nature or habit :
BELONGING BY NATURE
Since you lose your NATURAL physical characteristics, seems plain to me that you would ALSO lose your INHERENT ability score increases...