It begs the question, what is the accuracy of measuring radiation for a short interval, reviewing the decay and then extropolating that to a billion or more years....
That's not the way you do it. You select the isotope with a decay rate appropriate for the time interval of interest.
D = D0 + N(eλt − 1)
t is age of the sample,
D is number of atoms of the daughter isotope in the sample,
D0 is number of atoms of the daughter isotope in the original composition,
N is number of atoms of the parent isotope in the sample, and
λ is the decay constant of the parent isotope, equal to the inverse of the radioactive half-life
(from Radiometric dating - Wikipedia, the free encyclopedia
Your assumption of not steady-state deposition of elements is probably not too bad -- look at the K-T layer with it's sudden appearance of Iridium. However, even in that interval of massive introduction, the subsequent decay rate is stable The decay rate is independent of introduction.
Also from Wikipedia:
Dating with short-lived extinct radionuclides
Absolute radiometric dating requires a measurable fraction of parent nucleus to remain in the sample rock. For rocks dating back to the beginning of the solar system this requires extremely long lived parent isotopes, and thus the measurement of the different rocks exact ages becomes in-precise. To be able to distinguish the relative ages of rocks from such old material and get a better time resolution short-lived isotopes that are no longer present in the rock can be used. 
At the beginning of the solar system there were several relatively short-lived radionuclides like 26Al, 60Fe, 53Mn, and 129I present within the solar nebula. These radionuclides—possibly produced by the explosion of a supernova—are extinct today but their decay products can be detected in very old material
such as meteorites. Measuring the decay products of extinct radionuclides with a mass spectrometer and using isochronplots it is possible to determine relative ages between different events in the early history of the solar system. Dating methods based on extinct radionuclides can also be calibrated with the U-Pb method to give absolute ages. Thus both the approximate age and a high time resolution can be obtained. Generally a shorter half life leads to a higher time resolution at the expense of timescale.
The 129I - 129Xe chronometer
129I beta-decays to 129Xe with a half life of 17 million years. Since xenon is a volatile noble gas it can be assumed that there wasn't much of it in the rock to begin with. Since it is much rarer than iodine, it can be assumed that most of the 129Xe present in the rock is a by-product of 129I decay. By using the solar system's average xenon content as the natural abundance, the excess of 129Xe to the abundance of 129I ratio can be derived.
The 26Al - 26Mg chronometer
Another example of short-lived extinct radionuclide dating is the 26Al - 26Mg chronometer which can be used to estimate the relative ages of chondrules. 26Al decays to 26Mg with a half-life of 720 000 years. The dating is simply a question of finding the derivation from the natural abundance of 26Mg (the product of 26Al decay) in comparison with the ratio of the stable isotopes 27Al/24Mg.
The excess of 26Mg (often designated 26Mg* ) is found by comparing the 26Mg/27Mg ratio to that of other Solar System materials.
The 129I - 129Xe chronometer gives an estimate of the time period for formation of primitive meteorites of about 20 million years. Since some xenon might have escaped the rocks this formation period might be even shorter.
The 26Al - 26Mg chronometer on the other hand estimates a the formation time to only a few million years (1.4 million years for Chondrule formation)