No need to get to the crossover inside the speaker to accomplish the objective, it can be done with a lot less effort using an extra wire attached to the amplifier's speaker outputs or the speaker's inputs and then to the sub amp RCA inputs.
Do you think everyone that buys a powered subwoofer with speaker wire inputs has to open up their main speakers and attach a wire to the crossover low pass?
Absolutely not necessary, but if you happen to have speakers with external crossovers it can be done your way without extra effort, but with internal crossovers it is......certainly not hitting the easy button.
Here is my complicated way, whatever you do don't do it this other way that is easier.
(where is the hitting your head against a brick wall emoji?)
You still don't seem to get that some people are not inclined to diy such things and what is needed can be bought already made and ready to use for very little $.