In case you are not aware, all Assert statements (at least those in the ArtOfTest.Common.UnitTesting namespace) have an override with a parameter for an error message - this message will be output to log if the Assert fails. For example, Assert.IsTrue has 2 overrides:
public static void IsTrue(bool condition);
public static void IsTrue(bool condition, string message);
If you haven't already done so, you may want to check those out and see if you can use these to accomplish what you want to do.
But that said, I have a couple of comments that you may want to consider:
a) I am not sure I see the point of using Asserts if you are going to catch every exception - seems to me you are defeating the purpose of using Asserts and making your code unduly complicated in the process. If you are catching the exception so that the test does not fail, then a better way to implement it would be to not use Assert statements at all - instead, use simple if/else statements (use Log.WriteLine to log information and data to the log). Asserts are designed to be used when you want the test to fail if the condition is not met - yes, there are certain conditions under which you would wan the assert to fire and then catch the exception (but that should be rare in tests - more common in application code where you don't want the user to see every exception that is thrown).
b) Regarding the desire to continue on fail, the root cause of all your issues may be your design of having "one huge coded step test". I am assuming that means your test has only one step - which is a large coded step with many asserts in it. If so, I am not sure why you decided to implement it that way - but that is not an optimal test design because it is not easy to figure out where a test failed and why - without a lot of troubleshooting and digging around in the log file. You may be better off if you can break up that coded step into multiple small coded steps (each testing one condition). When you do this, don't catch the exception in these coded steps - instead, turn on Test Studio's Continue on Fail flag on those steps where you don't want the test to stop if they fail. This would make your code a lot simpler and smaller because you then wouldn't have to handle exceptions. You can use the first suggestion above to log assert failures to the log file.
Hope that helps. Please forgive me if I have misunderstood what you are trying to do.
p.s. I am not a Telerik employee but a long time user of Test Studio (specifically of the VS addin).