Yes the Salt Lake Farmers market at Pioneer Park is hugely successful, but the year round version has never been attempted. I think the Rio Grande Depot is the perfect place to start, yes people are used to coming to the farmers market on Saturdays and some on Tuesday's in the summer and early fall, but it will take a while for people to get used to having the option a few days a week, year round.
I think you could fit four vendors from east to west in the depot's main hall. One would be under each balcony and two in the middle back to back, two isle running north/south.
In this photo of the West Side Market

the narrow building to the left that extends behind the market as well, is the fresh produce building. The main building houses everything else, including an olive booth, candy, bread, cheese, meets, fresh fish and anything else you can think of.
West 25th Street, the street under construction in front of the market, is the heart of a neigborhood called Ohio City, and has a lot of restaurants, bars, and other retailers, but none of those are "market" type businesses.
I am sure that the state would be more than happy to have to relocate the historical society offices if they were getting rent from the market, or if the market. If a market here were a success, they could easily expand into the annex area to the south, currently housing offices, and the size of the plaza between the depot and the street could accomodate some small out buildings.