Is it appropriate to ask a professor how I may be able to improve my letter of recommendation?
I think it is okay to ask the question.  However, I do not think you should suggest that professors read your solutions since they are likely very busy.  

You may do better to tell the professors what you have been working on, including your GRE score, and then ask them if there is anything else you can do to prepare yourself for graduate school.  Then follow their suggestions.  Essentially it is the same question, but I think it could show you are a "deep learner" rather than a "strategic learner" who only cares about the letter.