Recommendations on Acoustic/Electric for Latin?

I just started playing with my first Latin cover band. I've never spent good time on a double, so I'm not quite ready to make the jump to an Ampeg baby bass. I would like to purchase an acoustic/electric bass to replicate that baby bass sound until I can make the leap with a big purchase. I'm looking for something with a big acoustic thump sound that also has reliable electronics. Most A/E basses I'm finding either have too thin of a sound (Ovation series) or the electronics are sketchy (Takamine GB30CE). (edit*) Or when plugged in they don't retain that acoustic tone.

For reference, I play on a G&L Jazz Bass 4 and a G&L Kiloton (when I want a humbucker). Both have the slim jazz width nut... I have smaller hands.

Any recommendations? Thanks!

 

Cool. Looks like it won't be too hard to demo one of these nearby.