Below is what our roofing expert John Stout from Go Roof Tune Up had to say in response to your question:
The most interesting questions are the ones without simple answers. You provided a very simple answer to your question. However, it is not what you are looking for.
Building a cricket would have the effect of moving the problem spot over a few feet. Is your problem with the accumulation of snow related to the snow load? Is the problem the accumulation of ice as snow melts? Icicles can be very beautiful, but destructive. Your gutter contractor can construct a custom fitted, heated gutter that could solve your problem.
A universal recommendation is to clean the gutters prior to the snow storm. Harry Helmet has a product at Helmet Heat that automatically prevents ice dams from forming. With a good strong gutter system along with the Helmet Heat (or similar) you may have a very satisfactory system.
Thank You for a very interesting Question! I hope this information steers you in the right direction.
Your Friends at Ask A Roofer