I think there were multiple 'assessments'. The ones deriving from G.O. 24 -- in 1861 -- were in the range of $10,000 each. The ones in the range of $300, I think, stemmed from a different order, proclamation or ordinance. Whatever the wording-scope of that one was [those were] later in 1862 is what is being 'nullifed' by the federal government in the communique you have nicely quoted here.
The distinctions between the two different assessments, I believe, would be an important one to make out of a full study of the matter. I believe that a different destination for the use of the funds was one important matter, and the different degree of supposed 'Southern Sympathy' was the other important matter. I hope I will be able to understand/articulate those distinctions when I have more facts and can sort them out.
I have now discovered a communication from the citizens of Southwest Missouri to the newly-appointed Major-General Commanding of the Department of Missouri [I think I previously mis-stated Halleck's command as Department of The West, but after Frémont's failures and sacking, the territorial assignments ordered out by McClellan were different.], specifically complaining about their state of affairs and strongly suggesting that the 'bad guys' be made to pay for their situation 'down there'. So, now reading California lawyer Halleck's G.O. #24 takes on some additional clarity when you see that, in some respects, he just turned around and created assessments almost exactly of the sort requested by the citizen letter he had received. [I am not sure on the timing, but this is just about the time he is sending Cump Sherman 'down there' for a military assessment, so by time he invents his method for financing his war effort, he has both military and civilian inputs.]