There's as much evidence for the actual tablets as there is for Book of Mormon described units. The repeating of accounts by secondary sources drawing from the initial account of something doesn't make it (the initial) more true or valid.
There's evidence for the Book of Mormon units in that the units offered would permit the users of those units as currency an efficiency and elegancy beyond even today's monetary divisions in terms of minimizing the number of coins needed to designate a specific quantity. Here's a tid bit detailing the elegancy of the system--
The Numerical Elegance of the Nephite System
The mathematical configuration of the Nephite system of weights and measures is intriguing. The main Nephite gold values were these: the senine; two senines made a seon; two seons made a shum; and the limnah was the sum of them all. In other words, the values were one, two, four, and seven (one plus two plus four), as shown on Table 1:
TABLE 1: GOLD
1 = senine
2 = seon
4 = shum
7 = limnah
Similarly, the silver values were also one, two, four and seven, as shown on Table 2:
TABLE 2: SILVER
1 = senum
2 = amnor
4 = ezrom
7 = onti
The beauty of this mathematical configuration is its simplicity.* The values of 1, 2, 4, and 7 can be expressed with the use of a single piece, and the values 3, 5, 6, 8, 9, 11, and 14 can be achieved with only two, while values of 10, 12, 13, 15, 16, and 18 can all be formed by using only 3 in combination. Not until one exceeds 13 does one need two of the same weights:
TABLE 3
Values
Number of Weights Required to Make up that Value
1___1
2___1
3___2___2 + 1
4___1
5___2___4 + 1
6___2___4 + 2
7___1
8___2___7 + 1
9___2___7 + 2
10__3___7 + 2 + 1
11__2___7 + 4
12__3___7 + 4 + 1
13__3___7 + 4 + 2
14__2___7 + 7
15__3___7 + 7 + 1
16__3___7 + 7 + 2
17__4___7 + 7 + 2 + 1
18__3___7 + 7 + 4
19__4___7 + 7 + 4 + 1
20__4___7 + 7 + 4 + 2
1. For a comparison of 1–2–4–7, 1–2–4–8, and 1–2–5–10 systems, see Richard P. Smith, "The Nephite Monetary System," Improvement Era 57, May 1954, 316–17. On binary systems generally, see Phylis and Philip Morrison, "Wonders," Scientific American (February 1996): 130–31.
The Numerical Elegance of the Nephite System (part 2)
The gold antion (worth one and a half gold senines) allows the system to express half values. The question is, why was "a half senine" not adopted? Perhaps for two reasons: smaller valued silver weights were used, but gold was probably intrinsically more valuable, and thus a piece of gold smaller than a senine may have gotten lost or damaged too easily. But more than that, the values of 1 1/2, 3, 3 1/2, and 5 1/2 more readily formed with the antion than if, instead, a hypothetical half senine gold measure had been used, as seen on Table 4
*
TABLE 4
Values__With the Antion_______Without the Antion__With 1/2 Senine
1 1/2___1 weight__________________impossible______2 weights
2 1/2___2 weights___1 + 1 1/2____impossible_______2 weights
3 1/2___2 weights___2 + 1 1/2____impossible_______3 weights
4 1/2___3 weights_1 + 2 + 1 1/2__impossible_______3 weights
5 1/2___2 weights__4 + 1 1/2_____impossible_______3 weights
6 1/2___3 weights_4 + 1 + 1 1/2__impossible_______3 weights
So, the presence of the gold antion improved the efficiency of the system. Again, all of the half values between one and seven can be made without needing to use two of the same weights.
Altogether, seven silver measures were used. The shiblon, shiblum, and leah were 1/2, 1/4, and 1/8 of a senum, respectively. Because these three smaller measures extend the binary system on into fractions smaller than one, one can see the mathematical consistency of the system from the leah to the ezrom. For purposes of clarification, if one were to consider the leah (the smallest measure) as 1, then the shiblum (twice the size of a leah) becomes 2, the shiblon becomes 4, the senum is then 8, the amnor 16, and the ezrom 32. See table 5, which also expresses this relationship in terms of powers of two and fractions, alternative ways of saying the same thing:
TABLE 5
1/8_____= leah_______= 1____= 2^0
1/4_____= shiblum___= 2____= 2^1
1/2_____= shiblon____= 4____= 2^2
1________= senum____= 8____=2^3
2________= amnor____= 16___= 2^4
4________= ezrom_____= 32___= 2^5
7________=onti
When Alma 11:13 says that an onti was "as great as them all," it would appear that the onti equaled 1 + 2 + 4 = 7 senums. It is possible, however, that the onti also included the value of the three smaller measures as well, in which case the onti was worth seven and 7/8 senums, or 63 leahs.
--taken from
http://farms.byu.edu/display.php?table=jbms&id=198
There you are, we may not have yet found coins but the system itself, through it's efficiencies demonstrates it wasn't just thrown in to some copy and paste work.
