Get practice moving before the cast bar finishes. Casters think their feet have to be rooted to the ground forever; they don't. The issue of movement is only a problem for non-stop or very rapid movement (like say, Titan EX double plumes). In most other cases you only knock off .5 to 1 second of dodging from your casting routine.

Anyone saying BLM is the "worst" DPS to bring to any content is either a terrible BLM themselves or has only ever played with subpar BLMs.