Crawfords Battalion existed as a individual command during the Battle of Arkansas Post when a number of them were captured. Those who were not captured either at St Charles or Sulphur Springs were consolidated into Dawson's/Hardy's 19th and 24th Consolidated infantry by February 1863. That would have left Lt Col Crawford with his infantry command. I don't think he "resigned" so much as he was reassigned.
Most of the Cavalry in Arkansas had been disbanded in the summer of 1862 because of the lack of fodder for the animals and the need for infantry at the time. But by early 1863 the realization had become appearent that there was a pressing need for organized Cavalry. I don't see Bill Crawford as following his personal ambitions so much as following orders to filling a need in the military structure.