obviously the most important part of any speed program is sprinting fast, so id just do what u believe in. personally i like weights in the program just because my 55 competition tends to be much more heavily muscled than i am. im decently strong (squat 2x my BW to parallel) and would rather beat them in the dash than be bigger than them, but i think evening out the strength advantage could be beneficial for me. plus my squat and my clean are my only two heavy lifts, im pretty weak in most other aspects of the weightroom
personally im not a fan of agility stuff outside of like position specific training just because agility work usually ends up involving ladders or some type of device that forces u into a stride length. plus i once read charlie telling someone that too much directional change work can actually loosen ankle tendons/ligaments and could be detrimental to agility (something along those lines)
what do you mean by strength inadequate? if you’re playing football u cant possibly be too weak or you’d get trucked. and how long have u been doing speed training/how is your program going so far?