An E2 serum level of 303 pg/ml is high... but not super high by any means. Many docs like to keep their MTF patients E2 level between 100-150 pg/ml. I've talked to more than 1 or 2 docs that ascribe to this protocol. I don't agree with it personally. You will not get the most benefit from HRT this way, it's slower, perhaps safer, but the docs of this mind set are usually more concerned about you developing any side effects. Basically, they are more concerned about getting sued than helping you.
From your response I take it you are not on any AA (like Spiro, Androcur, et al). I also do not agree with this protocol either, although many endocrinologists who treat MTF patients do. I have a deep background in medicine and science and as with all things in life, if you ask 4 different people the same question, you most likely will get 4 different answers. Just because you asked 4 different doctors the same question, don't expect the results to be any different.
I generally like to keep my E2 level between 150-200 pg/ml (if it shot up to 300 pg/ml for a month or so I wouldn't worry, but I'd get it tested again in 2 weeks, and lower my dosage if it remained there). I like to keep my total T at 40 ng/dl or lower. If it was lower than 15 ng/dl, I'd cut back on my AA to keep it around 20-40 ng/dl. Also not sure if your doc mentioned the importance of monitoring your potassium levels (especially if on Spironolactone) and liver function (monitoring liver hormone levels)... but checking these 2 things is also very important.