Your score would not come back until mid Sept and that is when schools will first put you in queue for initial screen then get screened and/or get secondary set, fill secondary and return, have all LORs in place, and then only get in queue for evaluation. By that time it is past October 1st, likely October past Oct 15th, so by the time you get evaluated, then reviewed by the committee, it would be late for decreasing number of interview slots.
My standard line for being complete by Sept 30 is based on the assumption that applicants have a reasonable normal time frame for items prior