Hi, Welcome to JustAnswer.com, I am glad you are here! My name is Eric & I will endeavor to answer your question.
If your dimmer is controlling a low voltage transformer which in turn is converting 120 VAC to 12 volts to power the lights, you can not use a regular incandescent dimmer on the transformer. You have to buy a dimmer made to control an electronic low voltage transformer.
You probably have 18 or 16 ga. cord and whereby I might have used a heavier ga. (14), considering your short lengths, that should not cause enough of a bump in your resistance to blow a 2A fuse. Honestly, I have never encountered this in the 27 years I have been doing LV lighting.
My recommendation is to try another brand of dimmer. I like Lutron (especially the Maestro series) and have installed hundreds of them with great success!
If you wind up calling Hampton Bay and they are able to actually offer a solution, please post back and let me know what they said!