I think I am getting more what you are saying, especially since this is for TRT, not supraphysiological doses/effects. SHBG may actually have a purpose which is to transport T,E2, or DHT to "at need androgen receptors" in this case. So, yes, you may get SOME relief of E2 and DHT symptoms in this scenario due to them being bound and non-active, the thing is you will EVENTUALLY have to process these hormones though. My understanding is that if the SHBG doesn't get rid of the hormone by it binding to a higher affinity androgen receptor, some fall off during pass 1 liver, and most hormones fall off and become bioavailable by pass 2 liver.
I feel like I threw a bunch of information at you, here is the thing, you are correct as far as I can understand it. The thing is I will have to take this a different route so it is more specific to you. What is your free T on TRT? If it is normal, more SHBG would cause the bioavailable (Free T) to decrease causing symptoms of low T at the same dose. Studies now recognize Free T as being the better determiner for TRT replacement than total T. So you taking 200mg per example would feel like 100 mg if you raised your shbg, less sides, but only because you have less bioavailable. It takes a lot to pull those hormones off SHBG the receptor affinity would have to be high, and like I had said DHT and E2 are gonna be the ones more than likely pulled off first due to their molarity and affinity for androgen receptors.
I understand healthcare is awful, I appreciate your service man!
I think you need to really look at this differently SHBG is not going to be able to be influenced much. I hear coffee can raise SHBG, doubtful it would be significant though. You may be better off dealing with issues more singularly. At the end of the day, your free T and aromatization are the problem... DHT you are kinda stuck with unless you take a 5a reductase inhibitor which like you had said previously can be awful for sides... The medicine is pretty clear on all of this, if you are interested in supplements that are NOT tested as rigorously for FDA approval that is a different conversation.
Sorry for this cluster fuck of a post, essentially the gist is I do not think raising your SHBG will do much . Even if SHBG would help relieve some of your symptoms a little bit, raising shbg is impractical and not going to happen in a significant or safe way.