It's odd what you say about the bootstrap circuit not performing well above D=0.5. I'm using the same driver chip for a hefty 200 watt power supply where the duty range is quite wide and I've never seen this happening.
I'm switching at 100 kHz - maybe you are using a switch frequency that is too low? Too low a frequency will cause bootstrap power to be a problem.
Another alternative is to use something like a little 2 watt Traco-Power or XP or Murata mini-power module to generate a floating 12 volt for your top FET.
A bit of housekeeping: The charge pump controller you found (LM2767) is only good up to a VCC of 12V. I did some quick searching, and I wasn't able to find one that works. But that's a minor detail, I'll move on to your main question, assuming that you can generate that 24VDC.
If you have 24V available as drawn, the gate driver and top power MOSFET will be in a race to see which blows up first. Your gate is rated for 20V, and your gate driver is rated for 16V, meaning the first time the high-side device turns off, the gate driver will blow. If the gate driver doesn't blow, then the gate will as soon as the gate driver puts the full 24V on to the gate.
My first question back to you is "Are you really sure you need a boost to your bootstrap capacitor?" Looking at the MOSFETs, you don't see a significant decrease in Rds(on) above 7V, so lets see how long it takes to go from your fully charged bootstrap voltage down to 7V (and you can calculate for lower as necessary). From your gate driver datasheet, the
quiescent current is 35µA at 12V nominal, resulting in
\$35\mu A=C\dfrac{5V}{t_{on}} \$ or \$t_{on}=C \dfrac{5V}{35\mu A}\$ which comes out to about 142 ms per 1 µF of capacitance. If you're holding the voltage high for a long period of time (multiple seconds), then a boost is necessary.
Since you only need a bit of current, you might be able to put a resistor (e.g. 100kΩ) in series with your 24V source, and a 12V zener diode across your high-side FET.
Another option is to have a high-side PNP set to switch on when your output is high.
Another option may be to have a small boost converter (charge-pump or inductor) that is enabled when the output is high.
The easy way to "just handle" this problem is to get an isolated DC-DC converter to provide a dedicated high-side source, though that is also the most expensive option.
Best Answer
There are several kinds of high-side gate drivers.
A simple driver can achieve 100% duty cycle on a high-side PMOS. You get the disadvantages of a PMOS: higher RdsON, lower speed, higher FET cost. But it's simple, and driver cost is low, so the whole solution could end up a better compromise than the other options.
To drive a high side NMOS, a voltage higher than the power supply is necessary. If that isn't available, then one way is to use a bootstrap capacitor that is recharged then the low-side FET switches on and the high side FET switches off. This cannot achieve 100% duty cycle as the bootstrap cap must be recharged.
To generate the gate drive voltage above the power supply voltage, several options exist. A charge pump is a good option at low voltage, here is an example gate driver chip that does this. Unfortunately neither digikey nor mouser allow to search using this feature.
There is no bootstrap diode outside the chip or inside it, so if you want to quickly look through lots of datasheets this is what you need to look for, along with the words "charge pump".
I've also done it with a "hand-made" charge pump, basically a microcontroller GPIO output that feeds a diode voltage doubler. With this you can generate a voltage a bit above the power supply voltage, and that can be enough to drive the gate of a high side FET. If the GPIO stops switching, a pulldown resistor discharges the gate. Crummy and slow, but simple and cheap. With a 3V3 micro though, the two diode thresholds will probably lose too much voltage.
You could also use a higher voltage supply if that's available somewhere nearby.
If you need isolation from the driving circuitry, then another option is to use an isolated gate driver, and add a small isolated DC-DC power supply to generate the driver supply.
Another option is the photocell optocoupler, which is basically a LED and a tiny photocell in a chip. Lighting the LED will make the photocell generate a voltage, which can drive the gate of a FET. Output current is very low, so it is quite slow, but it is simple, does not generate any switching noise from a charge pump or an isolated power supply, and it is isolated. It's a good option if you use a pair of anti-series FETs to switch AC voltage.