I've been working with ultrasonic transducers for my last project with your exact application (separate transmit and receive modules). I used the SRF05 initially and then implemented my own ranger.
You can easily find transducers that operate up to 400V (from Mouser), so 20V isn't probably the actual limit. From my quick measurements, it seemed like the voltage at the receiver side increased linearly with the transmit voltage. Since you are not relying on receiving a reflected signal, you should receive a much larger voltage than these rangers work with. Theoretically you should be able to get more range.
A charge pump supplies low DC current, but you can always put a large capacitor to store the generated voltage. Since you transmit in bursts, the capacitor should be able to supply the current without the voltage drooping too much.
I'm not sure how you plan on driving the transducer, which behaves like a capacitor (mine was ~2000pF). I put a resistor in parallel with it to turn it into an RC-circuit. The trade-off in picking the resistance is in getting a clean, fast edge vs. current consumption.
Here's some good information about generating a higher supply voltage. They used a standard RS-232 chip, which is a pretty clever idea. You can get +/- 10V from 5V easily this way.
SRF04 Technical Documentation
Some more thoughts: In a single burst, you can send out more pulses which will increase the maximum range sensed. Also, increasing the gain on the receiver side will increase the maximum range, of course. This is why I ended up designing my own ranger, so I could customize these parameters.
I think it'd be worth trying the inductive driver if having 20Vp-p doesn't work out. You should be able to generate huge voltages but it's harder to design.
For reference, my application only needed 1m range, but needed to handle very wide beam angles. I drove the transducer using 0-12V. I had a gain of approximately 500 which was barely enough for 1m. For a narrower transducer beam angle, you probably wouldn't need as much gain.