Nothing wrong with Burlap if you get quality material it should be odourless, I use dyed burlap which I treat with a fire retardant. The open weave breathability and neutrality of its fibers make it ideal for use in studios.
$300 is rather modest for treatment costs IMO but if you just need a few absorber panels and will DIY, not unthinkable (I have a few thousand invested in sound treatment - but a purpose built Project studio is not everyones goal 
)
Apart from the burlap comment your advice is sage, and on the money so to say 