John S said
I have just been tasting the variety of medlar called "Kha Kheti".  James recommended it.  Thanks James.  It is from Georgia in Asia.  
They taste really good.  They are very small though.  They have a tart flavor.  They still have the same number of seeds, but the seeds are tiny also.  As such, I could never recommend them to process medlar pulp.  
They seem to ripen on the tree.  I could see them becoming dark, while already on the tree. So I checked them.  They were soft.  When I wiggled them, they came off easily, and were completely ripe, or bletted. Retro Bowl
I got them through the Clonal Germplasm Repository in Corvallis. I would encourage you to order them.
John S
PDX OR
  

Sounds delicious, John! Thanks for the tips on ripening and size.