Hello Jim,
Yes, you are correct that the Official Records and the book "Sherman's Forgotten Campaign" by Margie Riddle Bearss, the wife of Ed Bearss, are silent about the type of guns Battery K, 1st Illinois Light Artillery were equipped with during the Meridan Campaign in February, 1864. On pages 300 and 301 is a listing of all artillery units available for the camapign. You mention in your post 20 guns but this list gives a total of 80 guns. Also there are many more batteries listed than the few you mentioned. Among the mentioned batteries are 3rd Ind. LA, 9th Ind LA, 14th Ind LA, D 2nd Ill LA, C 1st Mo LA, M 1st MO LA, h 1st Mich LA, 3rd Ohio LA, 26th Ohio Btry, F 2nd Ill LA, 7th Btry Ohio LA, 15th Btry Ohio LA, 6th Btry Ind LA, 2nd Btry Iowa LA, E 1st Ill La, K 1st Ill LA. Battery K, 1st Illinois Light Artillery is listed as commanded by Lieut. Isaac Curtis during this campaign.

A note concerning the type of guns Battery K had(or may have had)for the Meridan Campaign. Volume 31, Serial 54, page 244, of the Official Records contains the records of the brief fighting at Collierville TN on November 3rd, 1863 by the cavalry brigade commanded by Colonel Edward Hatch and Chalmer's confederate cavalry. Hatch's brigade was part of Grierson's cavalry division of the forces commanded by General Andrew J Smith. In a report by Colonel Hatch, he describes the battery as equipped with four mountain howitzers. These guns can only be 12 pounder brass smoothbore mountain howitzers widely used by the union cavalry. In this action, the battery was commanded by Captain Jason B Smith. I believe these guns to be the type present in February 1864, with the battery.