Rule of Thumb:
If a design patter does not work to solve a problem - its a wrong design pattern. As far as being your class to big - remember if you put in your code into any other class it would not reduce the number of lines your session object to execute.
However - if you reexamine the design of your classes itself and see if OOAnal and OODesign could solve what you cannot it might be more helpful.
Well, you could keep the LessA and do create the LessA1, LessA2 and so on. Then you have only one association among FullA and LessA. And LessA associates with LessA1, LessA2, ..., according to the nature of entities it´s (LessA1, A2, ...) referring to. So LessA will be used to join these others Lesses, but won´t have intelligence. By this way, the 2000 lines of code will be distribute to LessA1, LessA2,.., wich has the intelligence presented in the old LessA. The new LessA will only "call" the services of the other Lesses (LessA1, LessA2, ...).
(Sorry my english. It´s not so good).