I have an Innova as well. While a Towa guage is a nice thing to have, I find I rarely need or use it. I do 99% of my tension adjusting by testing and sight. Review Jamie Wallen's You Tube video on setting tension. This is a good place to start, but I have found that my Innova tends to make better stitches with slightly tighter tension setting then Jamie recommends. But try his first!
https://www.youtube.com/watch?v=Q1mRhcquZTM Much better to start with looser tension, it will be easier to trouble shoot thread breakage/shredding issues. And there are a ton of threads on the market that will only run on really loose tension settings.
You also need to discern is your thread breaking by snapping or is it shredding? Shredding is pretty obvious to tell as the broken end is very ragged and it will often break a ply before snapping the strand of thread. The most common problem for shredding thread is too small a needle for the thread you are using.
Other things that can lead to shredded or breaking thread, a burr on your needle, a burr on the hook of your bobbin race or in the throat plate or on one of the guides, tension settings way too tight, quilt sandwich loaded too tight, going too fast or changing directions way too fast.
To check for burrs take a cotton ball or nylon stocking and lightly pull along the surface to see if it catches fibers. You can smooth it out with an Emory cloth. To check the needle hole in the throat plate run thread back and forth through it like you are flossing teeth only without as much force to see if you can feel it catching anywhere.
Just because the thread was shipped with your machine doesn't mean there isn't a problem with it. Thread manufacturers are not infallible and the occasional cone of "bad" thread can make it into the supply chain. Can you easily break this thread by hand? If so toss it, it is no good and use a different thread. I have yet to load any thread on my Innova that "the machine didn't like". I have found plenty that I didn't like. And at one point in time I got a Superior thread called Highlights that I loved the looks of (also had a sister thread that was variegated called Rainbow). That is the only thread I ever had chronic breakage problems with. Guess what, it wasn't me or my machine. The thread was a problem and Superior discontinued it because of all the problems people had with it breaking and shredding. I still have a couple of cones of it.
As others have stated, you may have the quilt sandwich loaded too tightly on the frame. To test push your finger up from the bottom of the sandwich. You should easily be able to grab you finger to the first knuckle with your other hand from the top. Hope this makes sense.
I can understand your frustration. Finding the right tension setting is usually a first time longarmer's biggest hurdle. It is a fussy process at first but after a short time it becomes second nature. And we check tension a LOT. I check with every bobbin change, every time I change thread color (even if it is the same brand of thread) and every time I advance the quilt. Every Single Time.