To be clear I'm not clear on this topic....if that makes sense.
The general answer will end up being experimenting. Will need to run bloods (you need to see how high your levels are), and try the different methods of elimination to see which / what works for you as the topic isn't fleshed out completely.
Cases seem rare and some think linked to prior AAS usage and or found in people who are very gyno sensitive. HGH induced gyno seems to be caused by it binding to prolactin receptors in breast tissue. As for as I know nothing can stop this binding. Letro wouldn't stop it, and caber / prami would simply reduce the amount of prolactin floating around and limits that amount of prolactin which ends up binding, but you still end up with the HGH binding. I don't understand the exact mechanism, nor does there seem to be a solid yes or no answer anywhere. It seems it can easily go both ways in terms of the root cause.
Rambling point being: There are two general approaches...one being estrogen related and the other being prolactin related as it can increase levels.
Keeping estrogen low which letro will do might help because the two combined the HGH binding to the prolactin receptors in the breast tissue / signals + the presence of estrogen can add to the tissue growth. How low to be effective...I'm not sure which goes back to the experimenting with numbers. You're going to have to see what works for you.
or
Running a low dose caber or prami to see if that somehow indeed helps. I'm not boned up on how the body functions but logic would tend to lead one to believe if HGH can increase prolactin levels then caber or prami would be wise choices.
Other minor point would be if it's faked with HCG. But assuming your source is solid then this wouldn't be a factor.
To be clear most who run HGH don't run into this problem, which is why it isn't an easy answer. To answer your question about the test, yes some run a low dose amount of test w/ the combo of the above and have had success. In the end I would lower my iu amount until I figure out how to fix it, and began trying the different methods while monitoring how those methods effect my numbers and results.