Two important, tiny details can improve your range immediately! The way you hold your horn: the best way to hold it (if you're not already...) is to have your pinky and ring finger of your left hand held UNDERNEATH your third valve trigger. By doing this you will even out the pressure on both your top and bottom lip. That way, when you get into the upper register, the pressure is getting placed more on the lower lip than the upper lip. It really does help ;)
Another tiny detail that most people over look when they are trying to 'improve their range' is tongue placement. A reason why lip slurres are told to help out your range is because of tongue placement. If you noticed, play a lip slurre and feel where how your tongue is moving. (if it isn't, then that is something to work on!). Your tongue will help out your lip slurres, which in the end will help out your range. Generally, for when I play anyway, I use my tongue in everything. It can help with tone as well!
Before I started focusing on these two things I could only play up to a D above the staff. But now after a month or two on really focusing on these two things, I've been getting my range up to GG. They really do help.
Also! Definitely, DEFINITELY follow the three strikes you're out rule!! You do NOT want to put yourself through ANY pain! :sshh: Good luck