Thank you so much. Hopefully you have documented your school searches with copies of tickets, emails confirming interviews and exchanges with Dept heads, etc. If you have documented your efforts to date and have included substantive information about your future appointments and inquiries with other potential schools and the program heads that would be sufficient grounds for your an extension to be granted.
Also, any emails you have exchanged with supervisors at school programs you still want to investigate would be helpful to submit, even now with the request still pending. you are on solid ground
If you had included in your statement of reasons for extension this documentation and how specialized your area of expertise is, that would also assist an adjudicator in understanding you have special needs in terms of a PhD program.
You did not say what your filing date was but you can anticipate at least 5 months of being allowed to remain here from the date you filed the I-539. That is the backlog period for adjusdication.
Obviously, if denied, you have no options to remain. There is no appeal
I would like to address your frustration with me. I have been doing this for 35 years. Many of the facts you gave were irrelevant to the USCIS adjudicator making a decision, such as your dogs and your child's athletics. Those are not relevant to your original intent of coming here to investigate schools and muddled the primary issues I needed to focus on to give you a solid and professional answer. My most sincere apologies for any undue anxiety I may have added to your already stressed state of mind. It was not my intent. I am a nit-picker and my professional ethics make me question anything I am not absolutely clear on. After all, this is a HUGE decision which will affect your life forever. I want to make sure I answer you with confidence that I totally understand your circumstances, needs, objectives, and all other relevant factors. Please forgive my quiries. They were with the best of intentions.
I trust that is what you want, a lawyer who looks at the RELEVANT facts that an officer at USCIS is going to review in coming to a conclusion. Giving you an "off the cuff" answer just to tell you what you may want to hear is wrong and unethical. I take pride in my work, hence the aggravating follow-up questions.