Does the "inversion method" work/is it possible to grow hair at a rate of 1-2 inches per month?

No, this is unlikely to increase hair growth. I suggest seeing a hair loss expert now to go over your condition and provide you information about your best treatment options. There are great non-invasive options like prp/progesterone which can help with hair regrowth and/or hair transplantation. See an expert. Best, Dr. Emer

Average normal hair grows at a rate of about an 1/2 inch per month. While anything in a world of billions of people is almost possible, this myth is pretty well busted. 
There are indeed many medical alternatives today that can help you. If it appears to be typical male pattern hair loss, my preferred methodology is to address the root of the problem by 1) finding out what your hormones are doing and adjust them so that the DHT is pushed down, then 2) start a PRP program, and 3) possibly add an extracellular matrix. 
If it is an autoimmune response, we'll have a bit more work to do. But again, it starts with getting to the root of the problem and correcting it. If the hair loss has not been more than a couple years ago, it will generally grow back once the disorder is addressed and hopefully corrected.
I hope I've helped.
Warmly,
Arbella Sarkis, MD        

There is no evidence that this benefits the scalp or hair growth. Hair loss is more about gene expression and altered protein synthesis than simply blood flow. 

I have had patients hang upside down dailyh for hours trying to get more blood to their scalp to save their hair and it failed.  Genetic hair loss happens because genes interact with DHT in men