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I doubt it really answers your question, but I'd shorten the test to a single situation so that you don't need to wrap some code into a delegate that you pass to Assert.DoesNotThrow. Then, just write the test without any assertions. A test that throws an unexpected exception will fail, so it will do what you want, and you'll get the full exception.
About 10%-ish of my tests work like this; no assertions at all, and method names like ThisOrThatShouldNeverThrow().
Another option, while debugging, is to run the test in a debugger (using TD.Net) and in Debug|Exceptions check some additional boxes so that the debugger stops when the exception is thrown.