you're not thinking going through the crossover backwards....once the signals go through the speaker elements, what does it matter what's in the path after that?....do we have actual experience with passive crossovers, or are we going off what we've read or what makes sense?.....
A capacitor's response to AC current dictates that as the frequency drops, the cap's impedance increases at a specific rate. A coil's response is for the impedance to rise as the frequency increases. Because of these characteristics, if the component is in series with the speaker, it doesn't really matter which terminal it's connected to- the positive is used for convention and to minimize confusion. In a series circuit, there's nowhere else for the signal to go, so it must pass through the filter and the voice coil. If you put another filter after the original and the voice coil, it completely changes the filter's effect because the added component will filter out what it can. If you add a cap, the values add and if you add a coil, you have made a bandpass filter. However, if the cap is filtering frequencies that are much higher than what the coil can pass, you won't hear what you want because the frequencies between them will have been removed. OTOH, this is exactly the kind of filter is used for a mid-range or mid-bass driver- it removes the bass frequencies that it won't reproduce well and could damage it, as well as the higher frequencies that it doesn't reproduce and will inevitably cause "beaming" or "lobing" issues. How steep the filter will be depends on the drivers, the designer's intent, budget and any other special considerations.
I don't know if "we" have experience with crossovers and while I don't have as much experience as some, I've been doing this kind of thing for over 30 years, much of that time doing car audio systems with all kinds of weird configurations which often required changing and designing crossovers, building all kinds of enclosures and then listening and using an RTA to verify the results. I designed and built the speakers I listen to in about '96 and they still make me very happy. However, in listening critically for so long, I can remain objective about how they sound because if I hear a problem, I make note of it and when I have the time/inclination, I fix it. They're mine and not something that I made for someone else, so it's not so much a matter of pride as an on-going experiment. If people hear them and rave, it's gravy on the icing and adds some validation that they actually sound good.
I don't know how much experimentation you have done with this stuff but for less than 50 bucks, you can buy some caps, coils, resistors, a woofer and a tweeter to try different configurations and listen for the results. This is best done with an amp that you don't really care about, in case the load goes too low or it can't handle what you throw at it. One thing I would also suggest is to connect a hand-held woofer to am amp with music playing, turn the volume to a moderate level and turn it so you're looking across the front edge of the speaker. It doesn't matter which side is front, but you want to notice the sensation of the positive pressure on one side and the negative on the other. Once you experience it, you may become sensitive to it and for that, I'll apologize in advance. The problem with being very sensitive to it is that you'll hear the same thing when you listen to speakers that have phase problems, either from the crossovers being badly designed, mis-wired or from reflected sound. From personal experience, if you decide to re-wire the crossovers in a pair of speakers that you use on a regular basis, do both at the same time- using one of each will not be pleasant because of the cancellations.
