Or you could consider
1)remove the things in front of the JBL cone
2)Put the new tweeter coaxially ( in place of the other things) and run the wire outside ( i.e. on the grill)
3) arrange a lowpass filter for the woofer
2b)Put the tweeter aside or above the oval speaker; probably is that what you want to do: have some treble since the speakers are located in a way that the treble frequencies are not directed to your ears?!
BTW this is a ( 1st order) series crossover for a woofer and a tweeter.
It can be done! The value of the components has to be carefully chosen
For a 2.3 Ω woofer the value of the coil will be pretty low, and the wire gauge low too ( 14 ? ). But I don't think it will work in a car environment, as the tweeter's voice coil is prone to burn easily, with just a cap for protection. Better to go 2nd order.
The woofer now works without any low pass filter, so it would benefit from some band limitation.
The tweeter isn't a 4 ohm load for the frequency range below the crossover point. It's likely that that JBLs will have a rising impedance at high frequencies. There isn't likely to be a problem with the load.