Hello Catherine,
There are FSC options that are low-hanging fruit that will cost 0-5% more, options that cost 5-20% more depending on vendor, and options that are very hard to source as FSC in particular regions. Finding project partners that have familiarity with FSC sourcing is very helpful if you have choices between sub-contractors to use for your project.
The database Mark Chen shared is a good resource. A significant amount of work is going into making sure FSC suppliers are on that database and able to update their profiles from the backend directly. You can sort out who holds inventory vs who is a custom order vendor.
Ultimately, it is helpful to design with FSC sourcing options in mind. For example, if you design with white fir dimensional lumber Collin’s Company sells a great FSC certified product in the PNW. Retailers and Distributors like Sustainable Northwest Wood and Elk Creek Forest Products are helpful if you are in this region. There are other good suppliers out there that can deliver at reasonable price points.
For perspective here is a case study that was done in partnership with firms in Oregon and Washington for the Meyer Memorial Trust HQ last year. MMT HQ Case Study