popsoles.co, .net, .org are available, and there appears to be a .shoes TLD as well. You may want to consider grabbing some of these.
In terms of mixed messages in branding, perhaps at this stage you could achieve the separation of brand and business while still keeping focus on your key product - something like "PopSoles by ShoeScience" or similar. Alternatively, PopSoles is "generic" enough that it could mean "popular shoes", so the name works as a company name.
My opinion (which matters 1000 times less than your opinion) is that you _do_ create a company name that is separate, and incorporate that, but keep it in the background.
Your marketing doesn't have to acknowledge that entity, and if you're pursuing funding you can pitch as a company that is focussed on PopSoles but has a grander vision for other product lines down the road. So your company could be something relatively generic like "Rouben Fashions" and you'd be OK. If you create products down the road that don't fit into PopSoles, you create another website and brand launch. If they're all rockets, you then roll them into an aggregation site that is your company, which then spins out into the individual brands. Proctor and Gamble has separate sites for products (e.g. bounty.ca) and you could do the same once that line is big enough to warrant.