I conducted a search “Wirz’s prisoner exchange petition” and found a couple of items worthy of checking further.

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In July 1864, Major Wirz paroled a group of Union prisoners so they could take a petition to Washington pleading for a resumption of the exchange system. As incredible as it may sound, President Lincoln refused to meet with the prisoners. Secretary of War Stanton did meet with the petitioners but the exchange system was still rejected. One Union prisoner later wrote: "When the Andersonville emissaries returned from Washington there was not one word about the exchange of Negro soldiers being in the way of our release." Another Union prisoner later stated: "There was not a Negro soldier in Andersonville or in any other prison for a considerable time. When they were captured they were either sent back to their old masters or put to work on rebel fortifications. The Washington authorities had concluded to stop the exchange before there were any Negro prisoners."
http://archiver.rootsweb.ancestry.com/th/read/ACWGREY/2007-09/1190483029

See also: https://books.google.com/books?id=94nIAwAAQBAJ&pg=PA265&lpg=PA265&dq=Wirz+prisoner+exchange+petition&source=bl&ots=EWFvJFZcjr&sig=GyXzMLEwQqk7_GMJsluS2igqJrg&hl=en&sa=X&ved=0ahUKEwifypjl9oHSAhWM34MKHQ1UAwk4ChDoAQggMAE#v=onepage&q=Wirz%20prisoner%20exchange%20petition&f=false p. 265

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Shortly after the trial of the ‘Andersonville Raiders’ was concluded Boate was chosen by Commandant Wirz to be part of a delegation that would be allowed leave the prison and travel north to meet with President Lincoln. The purpose of this delegation was to appeal for better conditions in the prison and a wholesale prisoner exchange. Boate was one of twenty-one men allowed to make the journey, and on the 7th August 1864 that were to be exchanged with a similar number of Confederate troops. Six of this group were to then meet the President bearing a petition that appealed for the Union authorities to allow supplies through to Andersonville and also calling for wholesale prisoner exchange. Boate fell ill before reaching Washington and passed the petition to another member of the delegation. The group never got to meet President Lincoln and the circumstances behind this failed envoy mission would be hotly debated hotly after the war. (8)
https://irishamericancivilwar.com/2015/05/06/edward-wellington-boate-the-andersonville-pow-who-came-to-the-defence-of-henry-wirz/

See also Testimony of Edward W. Boate,
https://books.google.com/books?id=SfELAAAAIAAJ&pg=PA314&lpg=PA314&dq=Wirz+prisoner+exchange+petition&source=bl&ots=fiXuyvSr2o&sig=1D9K20c0FAn_QU1vSJAatkuaVTc&hl=en&sa=X&ved=0ahUKEwix-d2P9IHSAhXprVQKHZscCj84ChDoAQgyMAQ#v=onepage&q=Wirz%20prisoner%20exchange%20petition&f=false p. 314

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He [Wirz] also released a delegation of sergeants to go to President Lincoln to successfully petition for restarting the prisoner exchange. (Bureaucratic failure, however, prevented the release until almost the end of the war, and the resulting movement of prisoners back and forth from Andersonville added to their suffering.)
http://www.civilwar.org/hallowed-ground-magazine/summer-2014/hell-hath-a-new-name.html