The point of removing the breech plug each time and then putting more anti seize on and replace it, is a very good idea. The trouble with leaving them in the rifle after shooting is they can seize up and become very hard if not impossible to remove at a later time. Even on the range, if I am going to be a while before cleaning, I take the breech plug out or loosen it a lot...

As for chemical cleaning.. sure you can clean your rifle with that. I use brake cleaner all the time. I just find it easier to take the rifle to the sink and scrub it out with some soap and water. After that I like to run solvent through the rifle and finally some alcohol which displaces water. Some dry patches to make sure it is dry, and then oil the rifle up.