Hi Ed,
I can weigh in with some personal experience as to laying the boat on it's side. I'm embarrassed to admit but one time that I went aground, the water level went down to about 1.5" at low tide. My boat was over the 45 degree angle as depicted in the above diagram. The water was over the toe rail almost to the coaming for hours. I was 100% sure that due to the heavy weight of the boat that as the tide came back, it would flood the boat before enough bouyancy was acheived to raise the boat off of it's side. I'm happy and amazed to report that this wasn't the case as the boat rose like an angel. Bless Carl Albergs design. BTW, it lay on the starboard side (galley side on my boat) and no water came in from the sink, but I did have some water in the bilge probably from the hull-deck joint being submerged for hours.
As to your question of removing the rudder at this angle, don't forget that the rudder has to drop down a few feet to clear the rudder post, you would have to dig a trench which might be difficult. I recently removed mine at anchor with a mask and snorkel which was easy. I was able to source a take-off rudder from someone who is parting out a commander. At this point I now have to replace the new rudder at anchor. I would love to have the boat hauled at this point to replace it, paint the bottom, remove the toilet and sink and glass the through hulls, but I can't move the boat till the rudder's back on. I dropped the rudder alone, but will need some help to raise the new one. I'll let you know how it goes.
Good luck,
Barry