You could also try alternating between 4KHz and 8KHz. Slow enough to hear the back and forth change in pitch. Much louder, IME. 8KHz will be an octave higher, and will also be a resonating frequency. Alternating really fast to mix up and alter the waveforms can make some crunchy sounding chirps that can also be subjectively louder, too. Some experimentation with frequencies may be needed. Not sure why this is the case, but most all alarms and sirens use more than a single frequency. It definitely works, IMO. Something about how the brain works, I guess. Like the eye it maybe detects changes better than absolute intensity.
An easy way of increasing the driving voltage for a piezo is adding an inductor in parallel. If you replace the resistor+diode with an small inductor (a couple of 100uH to 1mH), the voltage at the piezo will be much higher, making it much louder. It basically forms a step-up converter.
This is neat. Will have to try this.
First order of business, though, is to make sure you searched for available buzzers in the current footprint. They aren't all created equally. I would order one of each with most promising specs. A dozen or so, if possible, and do some testing. Results may be surprising. Maybe OP should also try 12V element if you are going to boost voltage. An enclosed 3.3V piezo maybe won't necessarily get much louder with more voltage, because of how it's built.
I have used the thin plastic housing as speaker. Adhere the bare piezo disc onto the inside of the housing. Then a hole isn't needed to allow the sound waves to exit. They are formed by the housing. Added assembly cost is an added concern, but at least you reduce size of pcb, a little bit, and in some cases can use a much larger element. Mainly I suppose useful if you want to make device very small.
High pitch 4KHz piezo element creates tiny sound wave, and the housing will suppress/absorb/block a lot of it, sans a hole. Hole doesn't need to be very big, at all.