I longarm on an Innova and I have no issues with batiks. I have made quilts out of nothing but batiks but usually I am mixing batiks with regular quilting cottons. It is rare for me to make a quilt with no batiks. I have never had a needle break due to the fabric, it is usually doing something stupid like hitting a ruler. It makes me wonder what your LAer is doing or what kind of machine she has that she is having such issues. I have heard some longarmers complain that they have tension issues on them but I don't find I have these issues.
Some people say they can be difficult to needle (with hand work) due to the fabric being so dense. This is a result of what the greige goods goes through as it is being waxed and dyed and it is subjected to boiling water to remove the wax so it shrinks up as a pretty dense weave. True, it is easier to manipulate a needle through traditional woven quilt prints but the difference to me is negligible so I won't give up using them. I actually love them for applique because they don't ravel as easily and they are fabulous for raw edge fusible applique that is machine stitched down.
But if you are experiencing a lot of problems with them and not willing to find a new longarmer who is willing to work with them, your only option is to do hand dyes, either your own or purchased.