The 1882 Executive Order establishes the Hualapai Reservation "to and along" the river. Thats the 1882 river. It was not mapped.
The river channel was mapped before Hoover dam was built; call it the 1923 river, a now buried, and for any but the longest term uses, unrecoverable channel in most of the last 40 miles of the Grand Canyon.
The reservoir has been at intermediate and even maximum elevations, where it was trapping silt and filling in channels, and creating land on top of the old banks and the old channel. Call this the 1983 (maximum) river. Even though the USGS quads were produced before 1983, I believe they were intended to show the theoretical maximum, along with something that probably(?) is supposed(?) to approximate(?) the 1923 channel.
The river now is in the grip of another current prolonged drought, bringing the river back to a condition of flowing and carving into the silt, many miles beyond the Grand Wash Cliffs. The result is a channel that may or may not be exactly that of the 1882 or 1923 river. Call it the 2010 river.
The river in 1882 and up until Hoover went into operation fluctuated seasonally, ranging from a few thousand cfs to 300,000+ cfs.
Hoover's operation and the Colorado's water supply produce fluctuations in Mead reservoir over a multi-year period.
With Glen's operations, beginning in the mid-1960's, daily fluctuations become possible, although attenuated by the time they reach the reservoir backwater.
The purpose of the 1975 Enlargement Act with respect to the river was to unify administration of its use under Grand Canyon National Park. To that end, the boundary was put "on the south bank". That was in order to include the entire river surface in the Park, as emphasized in the legislative documents, and is a refinement, a definition, by Congress of what the language of the 1882 reservation proclamation meant by "to and along the river".
No one intended to take any of the Hualapai Reservation into the Park. This was qualified by language that land could be taken if the Hualapai consented. This, however, is a meaningless clause, since it was clear from the history of the LMNRA legislation that the Hualapai have fought hard enough for their reservation that they have no intention of agreeing to any violations of its integrity. This leads to the wet foot/dry foot doctrine: If you step off a boat on the river in the Canyon, and your foot goes into water, you are in the Park. If you step off onto land (even squelchy mud right next to the river) on the south bank along the Hualapai Reservation, you are on Hualapai land. The doctrine is a sensible, practical way of letting people know whose jurisdiction they are under, avoiding fencing and signs and court battles. It may be, for fiercely territorial types, a funny sort of boundary, since it fluctuates due to Glen Canyon dam operations. However, it is always well-defined, and good will prevailing, will serve the purpose.
The wet foot/dry foot doctrine is quite clear in its application until we get down into the reservoir-impacted stretch: Congressional intent was to reserve the administration of the river, regulating the use of its water surface, to GCNP. It is clear that there was no intent to take Hualapai land, and the EO language of "to and along" certainly is compatible with the wet foot/dry foot doctrine. Congress did not adopt either of the extremist views: that the Reservation extended to the middle of the river, or that the Park boundary would go to the historic high water line on the south shore. Neither extreme makes sense in terms of the practical aim of unifying administration over river use. What Congress did was exercise its powers to make specific what had been ambiguous. If one prefers, one can speak of Congressional compromise between extremes.
How, then, to depict the boundary? We cannot recover the 1882 river. The 1923 river is one snapshot of a fluctuating target. The prohibition (as I like to think of it) against taking any Hualapai land means that the maximum water surface as shown as of 1983 is irrelevant, because to depict that as the Park boundary would amount to acquisition-by-dam of Hualapai Reservation land, which the Hualapai have no intention of giving up.
We are left with the practical alternative, to take the depiction on the USGS quads of the "original" channel as an approximation of the 1882, 1923, and 2010 rivers. (The last, by the way, is also approximated by the Google map photographs, although they are not as up-to-date as 2010--see the lack of a rapid at Pierce Ferry. Another approximation.)
With these considerations in mind, I have settled on drawing the ---- + ----- + Park boundary by following the river edge line on the variously dated USGS quads. This line seems intended to indicate, "approximately", the river channel pre-dam, that is as of 1882, or 1923, or whenever the quad data was collected. In this way, the encroachment and silt pile-up on the south bank under previous high waters of the reservoir does not imply any taking of what was certainly, and is certainly, Hualapai land. In the present river-flowing regime of the upper Hoover reservoir, the wet foot/dry foot doctrine is mostly fairly obvious. To mile 273.3, if you step on land on the south bank, you are on Hualapai land, even if it is onto silt or mud. And if the reservoir should rise again, and water should cover that silt, remember that all things change, and behave well.