Change breadcrumbs for product

I am having trouble understanding exactly what you are trying to do here. From the two linked screenshots, it appears you are not using your e-commerce plugin’s archives for the category archive. Additionally, it doesn’t look like you had some of the Breadcrumb NavXT settings correct for what you want given your e-commerce plugin.

However, from what I can tell from the linked page (“The page I need help with” URL), it seems like the site works more like what you are asking for when compared to the screenshots. One thing I did notice is you have the “Hierarchy Referer Influence” setting enabled (which causes the breadcrumb trail to use the product tag if coming from the product tag archive rather than picking the first product category). Is there something else you want this to do that it currently is not doing?

Would it be possible to control settings with Code Snippets?
Setting fields gives some values, which work as conditions. I think that thouse could control also with code snippets by setting page related conditions. But knowing what conditions to alter, what is the format of variables. Looking at the source can find the name of the field but it is apparently a part of an array.

if(is_someting() {// page related condition
breadcrumb-navxt['field_name']='';
}

If code snipped has big priority, it would be read last and the value defined by the snippet will be used instead of the value defined by setting for this plugin.

You should be able to intercept the settings via the normal WordPress hooks for when the bcn_options setting get pulled from the database (e.g. you should be able to hook into the option_bcn_options filter). However, While this is possible, I do not recommend it as there is no guarantee this will stay the same from version to version. If you’re tying to migrate settings from one site to another, you can use the export/import/reset functionality in the settings page (click the help tab).