Jacob, I did a quick look at official records as The Dix-Hill cartel was still in effect for those captured at Arkansas Post. The was a breakdown in the process long story,but, there is talk of sending the captured prisoners to Richmond instead of Vicksburg for exchange around Feb.4,1863. There is also talk about sending some prisoners to Arsenal Island(Rock Island)Jan 12,1863 but,there was no shelter there for prisoners.They still were sent. If he did die at Rock Island it would of been between Jan 12 and the exchange date educated guessing sometime in Feb..You can get his records above. You need to read Series II Chapter V "Prisoners of War and State" of the O.R..Read Jan.-Feb.1863 entries.
http://ebooks.library.cornell.edu/m/moawar//waro.html
God Bless Texas.Let us know what you find!