Tessem, B., Approximations for efficient computation in the theory of evidence, Artificial Intelligence 61,315-329, 1993.
http://www.sciencedirect.com/science/article/pii/00043702939... (behind Elsevier paywall)
 Bauer, M., Approximation Algorithms and Decision Making in the Dempster-Shafer Theory of Evidence--An Empirical study. International Journal of Approximate Reasoning, Volume 17, Issues 2–3, August–October 1997, Pages 217–237
The first one focuses on quantitative deviations while the second paper considers the qualitaty of a decision.
Let's say that you want to figure out the chance of the resurrection happening based on the evidence that a period book (the Bible) says it happens and a straighforward application of Bayes' Theorem. Let's temporarily ignore any uncertainty about when the Bible was actually written. I'm not actually trying to argue either of these cases here, so it's immaterial.
On the one hand, you could decide that the prior is 50% (we don't have any other evidence, and people come back from what at the time would be thought "dead" with some frequency in the modern world). You could sample the frequency of books purporting to be historical that mention resurrections (low) to get the background frequency of these books, and that if its central figure did rise from death, the Bible would almost certainly mention it. From this, you get a rather high probability that the resurrection occurred.
On the other hand, you could set a very low prior (because people don't seem to come back from death), sample the proportion of magical events in period literature (substantial) to get the background frequency, and agree that the Bible would mention a resurrection if it happened, and conclude a rather low probability.
The problem is the same as in the Drake equation: all of these probabilities are basically just guesses, as there is no good way to measure them in this case. The result is therefore based more on how you guess than on the math. Any framework of reasoning that is based on probability will have this problem when dealing with real world events.
There are at least six intractable problems, I can see.
* Defining the thing you're looking for (in your example you say 'what at the time would be thought "dead"' - that opens up the whole problem of excluding the middle, are the options only resurrection vs non-resurrection?)
* Calculating any particular probability without a direct frequentist correlate (the probability that the bible would mention a genuine resurrection, in your example).
* Choosing a frequentist correlate when they are available (the reference class problem).
* Determining the prior.
* Determining which posterior probabilities to include (to be accurate you have to include all relevant probabilities, but that's impossible in practice, there could be an almost infinite number of contributing factors, so the choice of what to include begs the question).
* For probabilities after the first, removing the correlation with previous probabilities (BT assumes that the influence of previous information is excluding from new information, because of the conditional probability, in practice this is almost possible to do).
Then there's the problem that, for small inputs, the error in BT is very large. If your calculations ever drop to low probabilities (unless you can put tight bounds on the error of everything you've done), you effectively lose all information in the calculation.
The problem with your point about BT 'should assign a high probability' is that when you're reasoning about messy real world situations, lacking objective, quantitative data, it isn't clear how you go about generating probabilities for most kinds of evidence. It is no coincidence that the cited examples tend to be somewhat frequentist. When you start having probabilities like "the probability the disciples would have lied about seeing Jesus" you're doomed already. Not to mention the fact that BT assumes you can exclude the middle, which runs up against problems of definition in real situations: what exactly does "Jesus didn't exist" mean? You can hide a lot of rabbits in that hat.
But anyway, this is getting way off the track for the OP, sorry for the derailing. tl;dr - it is hard to model the real world in mathematical models of epistemology.