This project you have in mind is one of the most cost-effective and rewarding of all the mods or upgrades you could do. The way you are talking is exactly the way to do it. Don't try and reinvent the wheel. Designing a crossover is very technical and very difficult, especially trying to improve on an already professional design.
Most all of the problems people have are due to changing values. The value of caps and inductors affects crossover points, changes the frequency each driver gets, and messes with the sound. Resistors are like volume controls used to turn the volume down on drivers that would other wise be too loud. Almost all the mistakes you hear about are people messing with these values. So measure and be very careful not to change any values.
Audiophiles love to talk about caps. In reality resistors and inductors are equally important. The better ones don't "change" the sound so much as reveal more of what already is there. As you go better and better (read, more expensive) they remove or distort less and less and so you get more and more of what was already there. This is for caps, resistors, and inductors.
Here is a good source for many different caps -
Here's one for resistors -
This isn't really comparative but gives some good info on inductors. Coils make a huge difference!
https://www.erseaudio.com/Products/FoilQCoils
Also if you look at my system page towards the end there are pictures of the crossover upgrade done on my Moab speakers. Several of us on the FB Owner's Group have done projects like this, to varying degrees. Everyone so far extremely happy. You will learn a lot. Good luck!