They don't even allow me to inquire my status

They don't even allow me to inquire my status because of the large amount of cases. I think I have nothing to do but to wait. This is my company's lawyer. I don't want to wait until the last minute and know that they couldn't mail my package on time. That's why I am preparing my own package right now and want to send it sometime in early August. However I am very concerned about sending two packages to USCIS, one from me, one from my lawyer. So I would be very much appreciated if anyone can have a look at my questions and provide some sugguestion. Thank you in advance.