What switching frequency are you targeting for the LM3409? What sort of on times and frequencies are you targeting for the LED? Can you show your schematic?
The datasheet shows much faster rise times than you're seeing here with PWM, so it could be a problem with component selection, or it could be that since you're presumably providing a fairly long off-time the low-power shutdown feature is being activated, and the long startup time is due to the part coming out of that mode and more or less starting from cold rather than just enabling the output. The datasheet doesn't really indicate what startup time from shutdown should be, or if it's different from the specified rise time in PWM operation. You could test this by applying a PWM signal and see if the behavior changes.
In some cases, using external PWM dimming may be preferable to using internal dimming with a switching converter. When using the EN pin for PWM dimming the converter has to bring the inductor current up from zero and then back down, which means the rise and fall times depend on the transient response capability of the whole thing. If you put a FET in parallel with the LED, you can turn the LED off by turning the FET on, effectively shorting out the LED. That allows the converter to continue operating and inductor current to continue flowing while the LED is off, allowing for much faster PWM, and since the output voltage is near zero when the FET is on very little power is consumed. However this is probably not necessary in your case unless you need very fast rise/fall times, and it certainly seems like you should be able to get far better performance with the converter using the enable pin than what you're seeing now.