Here are some mounting suggestions for tapestries, one of the suggestions is velcro. You could get industrial velcro. Also, you could sew or glue the soft side of the velcro to your muslin or canvas (whatever you decide to paint your mural on) and the stiffer (poky) side of the velcro could just be stapled to the studs in your wall. The holes from the staples are so tiny, so your landlord probably wouldn't notice the little holes along the top of the wall. The nice thing about the velcro idea is that you could use the velcro along the top, sides and bottom to give your piece a little more stability so it doesn't wave around if someone passes by it and prevent the cats from getting behind it.http://www.marlamallett.com/mounting.htm
I am actually moving this month into a place where I don't want to paint the walls and I am going to use this idea to put up something in the dining room (which is what made me search out murals on craftster in the first place). If I get around to it, I will post a pic on here.