I've found the immune mobs will usually refresh if you stay there just whacking away with melee, so my suggested method is to go to town, shrine something if needed and then head back in after ~3-5 seconds.
This is more true for the single element immune mobs, as they refresh more often. I used to deal with them just by bring a very cheap second type of charm with me, so if i'm running lights, i have a 100ee level 10/20/30/40/50 fire set which costs next to nothing.
In theory, all you need is the lights/wild heals with caster daggers, axes, staffs and robes, could even skip the heals tbh. But samurai/headhunter in particular are awful to cast on