What is the the easiest way to answer the "does it make a difference question"
I am going to rule out hacking my speakers crossovers - and assuming any significant number of people would hack theirs.
If you use external active crossovers, you must disconnect each driver from the speaker's internal crossover. You don't have to remove the board, but you must temporarily bypass it. If you use both the external and internal crossovers at the same time, it won't sound right.
Those 4 binding posts on the back of the speaker cabinet are wired to the internal crossover, so unless you also disconnect them, you can't use them. Probably the easiest way is to remove each of the drivers, run separate wires from them, and route them out of the speaker cabinet through the port vents.
Paradigm Studio 60 v3 speakers (see
Paradigm Reference Studio/60 v.3 loudspeaker | Stereophile.com) are a modified 2-way design, called a 2½-way speaker. There are two 7" woofers, one woofer (the lower black one) is rolled off by the crossover at 500 Hz, and the mid-woofer (kevlar or glass fiber?) works up to the tweeter crossover point just above 2 kHz.
The frequency response curve shown below is Figure 3 from that Stereophile review.
Fig.3 Paradigm Reference Studio/60 v.3, acoustic crossover (without grille) on HF axis at 50", with the complex sum of the woofer, midrange, and port nearfield responses (black). Also plotted are the nearfield responses of the midrange unit (red), woofer (blue), front port (magenta), and rear port (green)…
Several questions or problems come up:
In a 2½ way speaker, how are you going to divide the sound with your external active crossover? The crossover between the midwoofer and the tweeter should be easy, but what about the 500 Hz low pass filter for the black woofer? There may be a solution to that, but right now, I don't know it.
Because the midwoofer and lower woofer seem to have separate port vents (see above), it is possible that the cabinet is divided internally to provide separate compartments for each woofer. That adds to the complexity you will face.
You must protect the tweeter from getting unfiltered signals below about 1 kHz, or you risk damaging it. Right now the internal passive crossover does that. It should not be hard to set up the active crossover to do that, but remember that if you damage it, you have most likely voided the warranty.
Unless you are comfortable with assembling and wiring speakers, this may not be as easy as you hope.
But you can easily do your bi-amp test while using the speakers internal crossover and the existing bi-amp terminals on the back of the cabinet. Have you already have done that? (I didn't read this whole thread in detail.)