I was going to post my own strategy for doing this, but this one is similar to mine so I'll just comment.
All you need to do is run straight into the Reaper room and fall down, straight out of the hallway. You'll land between some pillars right at the base of the stairs. Cast Thirst, walk forward a bit so you can target the Reaper between the Shadowmen and Flamethrow him as you take a couple steps back. He'll never get a chance to attack you. Collect the Darkmoonstone from him or not, then stand right where you landed from above for a second or two (so your bloodstain appears there) and then run out of the room off the cliff. This way you start right back at the beginning of the level instead of having to go through the Nexus loading screens. Also, you can collect your bloodstain right away after dropping down before fighting the reaper so there's zero risk of you dying before picking all your souls up.