This is more similar than it first sounds... you're proposing a variant of ecommerce that includes production of the goods. You'd still start by identifying a product niche with strong demand. You'd begin with flexible but expensive production options, then automate incrementally as you figure out which products can scale. You'd invest in technology to help you maintain an advantage over other vendors.

This is actually very similar to how semi-custom cabinets are made and sold, aside from the web interface. There is a catalog of available cabinets, and each cabinet can be customized in a variety of ways. For example, you can order a drawer + cupboard base cabinet with 2 roll trays and finished left side. The cabinets are built to order, but from a standard set of parts. They're built in a factory and shipped to the job site fully assembled. (One big maker is Masterbrand, which like GM offers many similar products under a variety of sub-brands.)

Instead of the web, though, cabinet selections are typically made by a kitchen designer, because the customer is not sufficiently skilled to take responsibility that the items ordered will actually fit. This might be a problem in woodworking, though perhaps less so for furniture.