Since every mystery shopping company is a separate entity and since they do not share their resources, companies have no way of knowing that you work for other companies and have great ratings. They don't know whether or not you turn in your reports before deadline. Frankly, they don't care. What they care about is your track record with THEM. I know it's frustrating to get started and prove yourself, but that's how it works. Mystery shoppers are independent contractors running their own businesses. The mystery shopping companies are our customers. You will have to prove yourself with every new company. Some are harder than others.
Since you didn't identify the company you are trying to apply with, it's hard to give you advice, since the advice would vary depending on company. For example, if you were talking about Maritz, I would advise you to call them. They typically allow self-assign after you are manually assigned to your first few assignments. And they prefer to deal directly with shoppers by phone. Other companies prefer email. You might email the scheduler to let her know your interest. Did you receive a mass email from a scheduler announcing those jobs? Reply to that scheduler and explain that you are not a new shopper but you are new to her company and ask her to give you a chance.