Hello McComas,
As far as Pāṇini's grammar is concerned, the only difference between external sandhis and sandhis between members of a compound is that the sandhi is seen as obligatory within a compound, but not outside a compound. Having said that, the members of a compound are treated within Pāṇini's grammar as full pada-s or inflected words, where the inflections simply get deleted, and new inflections added to the compound as a whole. Therefore, the members of a compound as well as independent inflected words of a sentence have the same status as pada-s, and hence the same sandhi rules apply to them. The practice of writing Avagraha is not seen consistently in the manuscripts and printed texts and it is generally not shown within a compound, but the actual sandhis are the same. Best,