I think the difference is the wire. I think you said you are using 24 gauge wire that has a resistance of about 1.6 ohms. The wire I am using is 20 gauge, it has exactly haly the resistance. It's putting too much of a load on the transformer even after using the dimmer.
I want a HOT wire, so I'll be oredering a BIG transformer on Monday. I think the idea of a fuse is a good one. I'd rather blow a fuse than another transformer.