Then the principle reason for increasing bass size is tonal?
Maybe, maybe not. First off, who said that the body size needs to be increased? You'll find many bigger bodied basses but stick that neck on an average sized guitar body and the neck is going to hit the floor. There is an ergonomic thing going on as well, but that isn't the whole story.
The reproduction of lower frequencies requires a bigger body size, but it's not going increase volume much?
Who said so? That may or may not be true of speaker cabinets, I don't know enough about them to say but it's not true of acoustic stringed instruments. As I said you have a balancing act going on. There is a finite amount of energy in the string and an inefficient method of converting it to sound waves. How that is done to best effect is down to a balance of body size and the efficiency of the top and materials ability to transfer that energy.
Too big, heavy and stiff and it takes a lot of energy to get going. Too small and it can't shift enough air to be heard.
In that case, is the problem with a smaller-bodied bass projection? My Fender bass can compete with maybe a classical guitar, but it can't really be loud across a small room, but it's still better than the Ibanez basses I've tried.
Partly yes, from my experience the smaller the body the more directional the sound seems to be. I have no knowledge of acoustic research to back that up though, it is just an observation. A bigger body seems to project sound better than a smaller one. Too big and the whole thing gets muddy and almost "floppy". Some of the bigger double basses I've heard have had a horrible sound and projection.
In fact, I have trouble hearing the notes off those Ibanez acoustic basses a few feet away...
Perhaps the secret to this isn't a gigantic body, but a body design that can project notes more efficiently?
If you can crack that one you are on a winner. As I've said all along you are trying to take what is quite a small amount of energy in a vibrating string and get it to be heard above everything else. Think about it. All in all that acoustic bass does quite a good job of being heard at all.
In the end you would be better off trying to find a light, small bodied acoustic bass or stick bass and a decent onboard through a small acoustic amp. You don't need a lot of amplification but just enough to cut through. That way if you have bigger gigs you can plug in to the house system or PA. You simply won't find a bass that can do what you want acoustically. You still haven't really said what instruments you are competing with and what gigs your doing?
I gigged as part of a duo for years with my best mate who is a bass player. He'd play acoustic for some gigs but as soon as we had more than a dozen people there he'd mic up or plug in. I on the other hand could hit the strings harder and shout and still be heard. It took about twenty people for me to plug in.
