Forgive me if this comes across as a tad pedestrian, but I always thought IAO was a god name for Kether. Crowley mentions (somewhere, I apologize I don't remember exactly where) that Kether represents the so-called masculine trinity of Christianity, and that IAO is a representation of that triune masculine force. Yod, Aleph, and Ayin of course all correspond to particularly masculine concepts (Aleph perhaps being the least overt). In the tarot invocation to IAO to send HRU I always thought it was an invocation of the "Father" that the "Son" might be made manifest in the diviner's consciousness. HRU, as we all know, is an expression of Heru-Ra-Ha, who is, as someone mentioned, the symbol of the HGA who resides in Tiphareth. I am not well-versed in real ceremonial magick, but it seems odd to me to have a Tiphareth-based deity mandate a Tiphareth-level angel. Usually when one wants a lesser power to do their will they invoke its superior, not a force at the same level.
As far as HRU's traits, the letters Heh, Resh, and Vav add up to 211. In Crowley's Sepher Sephiroth he notes that 211 corresponds to "worthy," "a lion," "strong," "a flash; lightning," "a girdle," "a flood; Jeor," and "fear of the Lord." All of these can easily be seen as qualities of Ra-Hoor-Khuit, the HGA. Particularly intriguing is the direct correspondence to destructive revelation, much like XVI The Tower. I am not particularly great with Gematria, but perhaps we can also see 211 as being Wisdom applied to Magickal force (2 being Chokhmah, Wisdom, and 11 being the number of Magick) since it is not a number that can be divided. This might also even be significant, since as a prime number 211 is a number unique unto itself, and of course, "Who is like unto Thee among the gods?"
It has been my experience that by following this invocation my readings are much more accurate and much more profound. In fact, I believe that using this invocation has allowed me to use the tarot to attain some level of Knowledge and Conversation. Despite what people say about the "mercurial" nature of the tarot, I have found the readings I have done about myself since I started doing them years ago to all be consistent, and to continually be pointing me in a very specific direction of understanding. My readings have never proven inaccurate, nor have they ever been incoherent. So it seems to me at this point that the tarot, coupled with this sort of invocation, can certainly be used as a tool and method for contacting and coming to understand the HGA and its Will.
