I'm not sure if you need a frame with similar specs as much as you need a frame that will allow you to create the same riding position. After all you won't really be riding the bike when it's on the trainer, you'll just be spinning it. So qualities that affect the ride, like head tube angle, frame material, bb drop won't really matter.
For example, on my Wahoo Core I currently have a Bike Friday Pocket LLama. It is very different than, say, my Surly Krampus, but since my "riding" position on both both are the same it works fine.
I'd say as long as you can get the riding position the same any ole frame would probably work-- with one caveat:
If the seat tube angle is too steep on the trainer frame you might not be able to get you saddle in the same position as on you Hillborn. So watch for that.
Eric in Brooklyn