I too had read that account in the book that "there were only 5 men (from the 10th TN) that joined the Federal forces, so Mulligan seems to have exaggerated", but that is false. The five men listed from the 10th TN were Co. A John Conner, Co. E Patrick King, and from Co. K Michael Joyce, Patrick Carmody, & Michael Crane.
Here's what happened. I got my ancestors pension record, he was Sgt. Alpheus Brown Co. G 23rd Illinois, in this he claimed men in the company were former Confederate prisoners. I wanted to search out the men of his company that were present at the battle of Greenland Gap, WVA on 4/25/63 so I went to the National Archives to look at the individual service records for the men of his company. In these records were individual cards that stated if they were former Confederates and gave the company and regiment they had served. I wish I had more time to look closer at them as I may have missed some and in looking at all the companies in the regiment will probably show many more that served. These are the men in Co. G 23rd Illinois that were former Confederates and became "galvanized Yankees"
Martin Berry Co. E 10th TN
Valentine Conroy Co. C 10th TN
James Gannon Co. I 3rd TN
Michael Joyce Co. K 10th TN
John Moran Co. K 10th TN
Michael Moylan Co. B 2nd TN
John Walsh Co. F 10th TN