lol, I'll ignore the "fairly sanitary" part as this means totally different things from person to person 
Until healed I would move to newsprint. The cheesy substance is a mixture of urates and pus. Not a nice situation, and it sounds like it is in pretty poor condition. You are in the right direction with keeping it clean and trying to disinfect with betadine but I think the condition has surpassed the limits of this treatment. The water soaks in this case should be switched to hydrotherapy which is running water over the wound for 15minutes 2-4 times daily. Your description suggests the need for systemic antibiotics and definately a trip to the vet. Hopefully this snake is still feeding and your antibiotic prescription can be given orally. The prognosis for a good recovery should be great with the above course of action. Anything less will see a much more questionable outcome.
Good luck, I'm sure he'll do fine 