Firstly, is it possible that you could post the text of the message that you received in your google WMT account telling you they were doorway pages?
Secondly, prior to the penalization, how much traffic did the "general sporting goods store" get in relationship to the other niche specific sites.
How strong is the branding of your general sporting goods store compared to the individual niche sites?
How does the backlink profile of the general sporting goods store compare to the other sites?
If the product photos and descriptions on the niche sites are the same as on the main site, they might have been in competition with one another anyway. It's possible that setup may have been hurting your rankings for some specific products.
It may be a better idea to 301 the appropriate pages of the individual niche sites to the main sporting goods store. We know that google is giving more and more love to "brands" and to be honest, in your other promotional activities, it is going to be easier to promote one larger store than to promote 20 smaller stores.
I am just saying there is a possibility that google is dong you a long term favor / giving you a hint about what they want you to do by dinging your niche sites.