These statements pretty much tells you your doctors TRT knowledge is very poor. Once you stop injecting exogenous testosterone the effects wear off and you lose the benefits some time after stopping.
Your pituitary gland is responsible for testicles stimulation and therefore testosterone protuction.
At 1 month your levels are not stable, not until 6 weeks and if at anytime you change the dosage, levels will be in flux for another 6 weeks.
Here is your problem and while TRT failed, by injecting once weekly you were setup to fail because these large infrequent injections drive estrogen production. I don’t think twice weekly will be much different, your going to have to make bigger moves to see big improvements.
Also some men are sensitive to fluctuating hormone levels, my body ignores testosterone when injecting twice weekly if levels are declining for too long. I think this is another reason why TRT failed.
You need to monitor your FT and SHBG levels, you can’t start TRT without them and if you do so you will be in the dark and could possibly end up another TRT failure. I think you need to say goodbye to whoever is managing your TRT unless they are willing to work with you and learn or you’ll need locate a private doctor who prescribes TRT on a daily basis.