If your idea is so easily replicated that you fear losing first mover competitive advantage by rolling out a beta, then you probably need to reassess its viability as a business. You could also do a friends and family soft launch to get feedback and show viability.
Any e-commerce/membership site/app needs to demonstrate its interest across a large enough member/user base that it's interesting to investors, and you as an owner, for that matter. By not having the initial "pop" number of users, you are asking the investors (and yourself) to bet that it has legs with a large enough audience to be a viable business. Are you so sure it's such a good idea that it will have mass appeal? If so, then why do you need investor money? With today's social media, a viral launch is inexpensive, so requiring funding to advertise and preload a site launch seems unnecessary. Launch it - grow it, and go after investor money to scale it, not to start it.