Unplugged tone unobtainable ?

Today I've been playing a number of my instruments (not only bass) plugged in and unplugged.

Playing my Peavey TL-5, it struck me once again how much I would like to hear the acoustic sound amplified. Don't get me wrong, it has a nice electric tone, especially with the Bart soapbars and EMG preamp I installed but I would love to hear the hifi zing that it has unplugged, even with old strings.

I did try eqing my Telecaster looking for the same thing but only got most of the way there. I'm guessing it would take megabucks (more) in amplification to get what I want. A piezo gives a different sound again so that's not really an avenue.

Anyone else had this thought and if so, did you try to find the sound in amplification or another way?

Cheers

Tim