OK, I went out and got the same model neo-air mattress based on the comments in this thread. What a difference! WOW!!! Yes, center of gravity is higher and it is slightly less stable, but not unmanageable. Best part is that there is NO repeat NO shoulder squeeze. I attribute the good points on this to the design of the neo-air with the air tubes going from side to side (unlike old inflateable airmattresses that go from head to toe. The mattress just fits the underside pocket, although the material of the mattress does not slide easily.
I'll be takeing this setup with me on my Hudson Valley bike ride this coming week (31 July - 5 August). I hope to find suitable sites to hammock. That is not always easy since the bike tours like to use schools or open parks where you can pitch lots of tents in limited space.
I hope to take photos and report back on my experiance.