Hi There + Welcome!
Adding a dedicated bass driver to the 604 would be a good idea.
I believe it could be made to sound great. The 2240 would add some nice ( + missing ) weight to the bottom end of the 604 system.
I would recommend the 604 in something like a 3.5 - 4.0cu'
sealed cabinet to emphasize that woofers transient response.
The JBL 2240H could be in something like 8cu'
ported box tuned to 35hz ( with a 3rd order LowPass filter set to roll-off a 50hz ) .
( IMHO ) I also believe it would be a pretty bad idea for an inexperienced builder to put it all into one mammoth cabinet without being able to know it will all work first ( by using test cabinets ).
- There's quite an
efficiency mismatch ( once the lowpass filter is in place ) between these 2 woofer types,
- This will necessitate the running of the JBL 18s off of a
separate amplifier ( ie; Bi-Amping ).
Here's a screen shot of WinISD prediction software showing that to get the 2240H
just to match the 604 level
takes more than twice as many watts ( hence the need to use a separate amp for the 18 incher).