Have you created classifications for the Product variable? I've found that this has been a big help when it comes to handling dimensions with a ton of values, such as Campaigns.
For example, let's say that the 300 products you referred to are "T-shirts". You could create a classification called "Product Category", and use "T-shirts" as one of the values when you upload the classifications. This will allow you to create a segment that will limit the Analysis Workspace table to only show "T-shirts".