TieDye, The mountaineering guide services lead groups up the MR often during March & April. They rope their clients on the MR, but most independent groups don't. This being a low-snow winter, you can probably go earlier than normal years. The Ebersbacher Ledges should be useable early, just not sure how early.
Getting a permit in April is easy since it is before the quota and lottery. In May, and even early June, there are always noshows for people who got a permit in the lottery. But I'm not sure if or how the no-shows permits might be made available. Everything is going online more and more, and making the noshows available online is something that they are working on.
I don't recall reading about anyone doing the duathlon you are working on. It's got to be a monumental effort! I once thought riding 100 miles in a day was huge, but now I know two guys locally who have completed double-centuries. Good luck, and we'd sure like to see a report afterwards.