I don't have a source that's likely to satisfy you - for two reasons.
1. Nobody has actually done a through, scientific carbon audit of the supply chain for these plants. You have napkin arguments in film, or on the internet, that you can trivially search for, that conclude this one way, or another, depending on their politics.
2. The carbon cost of running them is incredibly dependent on local conditions of the precise bits of wood that were sourced.
I can expand on the latter.
The hardest part about logging is getting your equipment to the logging site, building the roads to it, and then using those roads to get the logs out. I guess those are the three hardest parts about logging.
If you can cut down your logs, truck them only a few miles, toss them in a river, and then pick them up a hundred miles downstream, to load onto a barge, your carbon footprint is minimal.
If, on the other hand, you have to truck them 15 miles down logging roads, and then 90 miles down a freeway, your footprint greatly expands. (And has to include factors like building the logging roads to begin with.)
Unlike with mining, building logging roads is much harder than building roads to a mine - because you have to cover a lot more ground, to get an industrially useful amount of wood - compared to something like a pit mine. You have to use heavy equipment to drag logs over incredibly difficult, unroaded terrain, so that they can be loaded onto trucks that will go down the roads.