Modeling as Factless Fact or Dimension

I am trying to decide how to model product attributes that vary by store.  The attributes are product status, product type, program, etc... 

My original thought was to create a product status dimension, product type dimension, and program dimension that can be used on the various fact tables.  A reference to these would exist on each fact table that also has store and product.  This would satisfy the needs to be able to report on sales by product type or inventory by product status, for example.

However, we also want to be able to count the number of product/stores with a given status or type or program on a given date.  In order to do this I was thinking of creating a factless fact table with the following keys: product, store, status, type, program, start date, end date.  But this just feels like a type-2 dimension table to me.  Am I modeling the fact table incorrectly?  Does it make sense to create a product/store dimension instead of separate status, type, program dimensions?

Thanks