Yes there is a benefit to being a long-term user of Google Product Search. It will take time to gain traffic for any new website. Data quality plays a roll as well.
One thing to be very aware of is that duplicate content sent by the same seller is prohibited and can cause your products from either site to go offline. Luckily, if your products SKU up on comparison pages, and you are price competitive, it should not take you as long as other sellers with soft goods, or sellers that are not price competitive.
Another factor that will influence your traffic from your new website is that you will have 0 website reviews, so your site will seem not as safe as the other players with reviews.
Thanks for the reply, Andrew. It looks as though I'm going to have to have two sites with different content for each of the products, and let the new one grow on its own.
I'm still trying to find out how Google Shopping/Merchant/Whatever treats noindex tags. If I can keep my current individual product pages with their good Merchant rankings and customer reviews, but 301 redirect the main brand pages to the new site, I may be able to make growing the new site easier.