Depending on what kind of shell your after I guess here. heavy shot or weight shells seem sparce all over but I think its do to how long they last. Most stores buy out of them fast when they get them and turkey hunters all know so when they find them they buy a number of boxes of them at one time. The only two companies that seem to be out there are Hevi shot and Federal.
Winchester does not make a 20 gauge load with #6. As Joe says #5 will work as well, the only difference is your not going to get that shot count that 6 will give, but they are better then nil right