Series 1-VolXVII/1. Report of Charles Ellet, commanding the ram Monarch.
";and I kept up the river for 12 miles.(after passing Fort Hindmand)The water became so shallow as to render it impossible to proceed further. The Monarch got aground four times as it was."
I don't remember what the Monarch's draft was, but it was more than the Ironclad's and Tinclads. Still I doubt if Porter would risk having his gunboats stranded by shallow water. It was a fact that the Arkansas River would rise and fall significant amounts literally overnight. And even when there was enough water the lower Arkansas was considered extremely hazzardous to navigate due to snags and sandbars that would form overnight.
All that said, McClernand did want to advance, but Grant, in no uncertain terms told McClernand to return to Miliken's Bend for the operations around Vicksburg.