[Neil Mylar LakewoodCA]

Jeremy,
The unpainted part in your photos (which you are calling the dash rail, post and brackets) DO NOT come out. You do need to make sure that you have removed all the nuts and bolts that hold the tank to that assembly. You should be able to eventually pry the gas tank out. Double check that you got all the bolts.
I always stick a rag in the area at the bottom of the cowl so when I drop a bolt, nut or washer, it does not disappear. There are two bolts (one on each side) that are pretty much hidden.
The disadvantage of removing the gas tank only and not the lower cowl section too, is that the new cowl webbing will not be a continuous piece and might not show well. If you decide to remove the lower cowl too, there is a couple of rivets that will need to be removed at the bottom where it joins the body. You also might need to loosen and lift up on the body to pull the lower cowl out. It is a very tight fit to get it by the motor, too.

My recommendation would have been to tried the dirty leg cleaning method first. If you have not damaged the existing cowl webbing, you might want to reconsider removing the tank.