If I watch Cboot with the highside Mosfet held low, I get a steady 4.5V. Why would this not go up to the full 5V supply of the driver? Some kind of internal drop in their level-switcher-doodad?
Most often there is a diode connected between the supply pin and the boot pin and that is how the cap is charged. The free end is pulled low by the low side mosfet and the cap is charged to one diode drop below the supply voltage. The diode is usually a schottky to minimize voltage drop and some drivers require an external diode because it is hard to build a good internal schottky.
You should not have the 10k resistors on the high side mosfets.
What mosfets are you using?