Filter and FB are two different things. The filter node is an internal VREF node, with a modest impedance and noise level that can therefore benefit from a relatively bulky external capacitor. AFAIK, it is always ahead of the error amp, so plays no role in compensation, but acts to reduce the noise level at medium to high frequencies, and improve PSRR, to the extent the ref's PSRR is poor at least.
The small cap from output to FB, is a feed-forward, "speed up" or "zero" capacitor. It acts to increase negative feedback at high frequencies, improving transient response. The value is determined by error amp and pass device dynamics, which aren't ever published (for any regulator I've seen), so you're best using the recommended value, and the recommended Thevenin value of the resistor divider with which it acts. (Since the important part is actually the RC time constant of those three components together.) A smaller value (including zero) is likely fine, just with poorer response; a larger value may cause too much loop gain and thus oscillation.
I suppose it's also possible that the FB pin has some conductance itself, and the resistors/cap act against that as well; in this case, it wouldn't be strictly the external RC time constant, but also their value in relation to this value. (Imagine an example like, the FB pin happens to be the emitter input of a common-base amplifier.) I don't know that this is ever used either, just putting it out there as a possibility, for which such a connection would be important.
As for loudness, if it's not just gain but it's clipping at maximum and still not loud enough, yeah that's definitely a supply problem. It may be fruitful to just drop in a +/-5V or higher switching supply (might as well go bipolar for ease of use, eh?), and use it as an exercise in good filtering/shielding. Assuming you have the space to do so, of course; no idea how big this is, but it sounds like the kind of thing that could be quite small, and this would likely be a significant change in size.
Tim