I just came across this 2006 Smithsonian Magazine article about a breeder, named Harry Jan Swartz, who was trying to breed musk strawberry flavor into a modern berry.

His website, Five Aces Breeding doesn't seem to have been updated since 2007. Additionally, I couldn't connect to the web site of Ruby Mountain Nursery mentioned on that page.

I don't suppose anyone knows how that breeding program is going? In the Smithsonian article he predicts success is only "a few years away."