The No4 Enfields well have a flat face at the muzzle, some well have a slight bevel. I've seen plenty of LE's with crown damage but it's seldom caused by the cleaning rod.
A brass, aluminum or carbon fiber cleaning rod well not damage the muzzle. The steel is significantly harder than the rod. Typical steel cleaning rods seen in military service can wear the crown from years and years of constant cleaning these receive in military service.
I do clean all my precision barrels in the direction of bullet travel, but for mil-surps from the muzzle is fine. If you overly concerned about muzzle wear use a bore guide.