I haven't read Michael Forsyth's Red River Campaign of 1864 and the Loss by the Confederacy of the Civil War but comments by other reviewers suggest it is similar in scope to the works of Joiner and Brooksher. Forsyth's main thesis seems to be that historians generally underestimate the consequences of a more decisive Confederate victory, one that was far more likely to occur if Kirby Smith had not diverted his infantry to face the other Union force coming down from Arkansas.
Which brings me to Forsyth's companion volume (which I have read) called The Camden Expedition of 1864 and the Opportunity Lost by the Confederacy to Change the Civil War. This book summarizes the course of Frederick Steele's northern prong of the combined Union offensive and the Confederate efforts to thwart it before it reached Shreveport. Forsyth's study is the first book-length treatment of the expedition from origins to aftermath and is important on that score. It also has a fairly good description of the engagement at Prairie D'Ane. The progress of the Union expedition up to the capture of Camden is what is left out of Edwin C. Bearss' far better military study Steele's Retreat from Camden and the Battle of Jenkins Ferry (I believe the softcover edition of this book is now out of print as well). With his usual spare but highly effective style, Bearss provides the reader with a nice overview of the retreat from both sides along with detailed tactical studies and maps of the battles of Poison Spring, Marks Mill, and Jenkins Ferry. Both books complement each other fairly well.
Well, this concludes my Red River Roundup. I hope readers will find this list helpful. Of course, these entries are not meant to cite all works, just the most relevant ones that I would rate anywhere from middling to best. My lists will tend to leave out the poorest books dealing with the subject at hand (example here, Curt Anders' Disaster in Damp Sand).