TPS92512 quicker startup response during PWM dimming

I am using a TPS92512DGQ which is PWM dimmed. Typical frequency/dutycycle is 1 kHz/50%, so this is well within the specifications. During normal operation, I have got the device to work as intended.

However, in my application, the driver is activated intermittently, with long inactive periods between bursts of LED light. It is important that the LEDs output light immediately, on the first pulse in this burst.

This has proven to be a problem, since long inactive times mean that the BOOT capacitor (from PH/pin 10 to BOOT/pin 1) is slowly discharged. It takes 2-4 pulses on the PDIM input for the capacitor to charge enough to start switching the regulator inductor, and therefore there is a delay of a couple of milliseconds until the LEDs go on.

One way of solving this is to send very short pulses, for example single pulses of 100 us every second, which is barely noticable. This is, however, not a desirable solution.

Hence my questions:

1. Is there a way to improve the response time after a long time with an inactive PDIM input signal?
2. Can the BOOT node be "hot-wired", by having a voltage divider from VIN and a diode feed the BOOT node even when PDIM is low?
   1. Specifically: VIN = 24 V, resistor divider has a 100 kohm high resistor, a 33 kohm low resistor, which means the "charge" voltage will be 6 V assuming negligible current is consumed.
   2. Is there a risk of damaging the regulator if voltage is fed into the BOOT pin this way (the functional diagram in the datasheet does not clarify how this pin is connected when PDIM is low, I can't tell what's in the "BOOT Charge" block)?

For information, my BOOT capacitor is 100 nF, and the output capacitor is 4.7 µF. This fulfills the relationship between them defined in section 9.1.3.