Yeah Jim,
you are right: the final 'i' vowel of a.t.thahi is elided when this word is combined with aakaarehi. The point i wanted to highlight is that a.t.thahi has third case ending, the 'h' is not an inserted letter for euphony. If the term would be 'a.t.thaakaarehi', the 'hi' has been dropped - this is a samaasa.
For all:
If anyone is willing to learn the Kaccaayana Grammar, i am willing to post grammatical notes from kaccaayana, as far my time allows. Those interested, please tell me how i should post and what will help you.