You almost understand it.
Firstly - the pups don't 'hear' what 'the strings sound like' They are deaf to audible noise. They only respond (a bad word, but somewhat descriptive for the nonce) to the electrical flow from the fields being cut by the strings passing through that field - the Gauss effect.
The wood that you can feel vibrating is vibrating from the energy from the strings, now wandering around inside the body. This is resonance, and is subtractive. This sound you feel or can 'hear' with no amp, is in it's death throes and will not re-vibrate the strings no matter how much you may want it to.
Wood is passive and it is only acting that way with the energy that is being lost from the strings themselves.
There is no other form of energy in the wood (A wall plug? Batteries? A wound-up spring?) for it to maintain the vibrations and it just decays there.
Otherwise we'd have perpetual, motion and you DON'T want to go there - or do you?
It may feel like the wood is 'singing' when in reality it is just destroying the very sounds you might think are being somehow amplified.
Then by another stretch of imagination, somehow this energy is sent back through the bridge by causing it to vibrate again, to re-excite the strings into motion and there to cut the magnetic fields of the p'ups again.
That's backwards. This is not a two-way street!
Sound waves check in (to the body), but they don't check out!
Different bodies attenuate (the 'take-away part) certain frequencies or zones of frequencies (my term) and they are not all alike, that's a given and answers your thought about transplanting different p'ups into different bodies.
That's correct they way you stated it - almost. You didn't go far enough with your own reasoning to see that since the wood of the bodies attenuate different frequencies for their own inherent design, they indeed will sound different.
BUT not from amplification or support for any set of frequencies in the body itself.
On the contrary, they will remove certain ranges of notes, frequencies, etc., but only by their own individual ability to absorb the ones they can and leave the others un-absorbed.
This is why some persons actually believe that their particular body adds to the range of frequencies they say they do.
What really happens is that less-desirable freqs are absorbed and the frequencies that are left may sound as though they are reinforced, when they are really the freqs that are left out of the attenuation process.
This, of course assumes that the other variables* are all in spiritual alignment with the program and are either 1) capable or or 2) incapable of allowing the preferred sounds alone.
* Variables: wood, thickness thereof, moisture content, molecular adhesion to other grains in the wood, if the wood grew on the South side of a Peruvian hillock in a Southwesterly prevailing wind, and constitution of paint, sealers, finger prints and 'Funk' or 'Mojo' on the strings, neck, pickguard, screws holding the neck on, etc, etc, ad infinity.
