And how is that going to help, another 6mA of collector current?
Well, I've seen this problem before, with a similar circuit using 2 IR leds in series in a communication circuit for a measuring device. Its just the intrinsic capacitance and low "switching speed" of most leds. Also, the circuit is open-collector, which inherently has fast turn-on and slow rise time.
The 1K is strong, but I assume the circuit won't be battery powered (an adapter is used). If so, then 4.7-10K may work. An oscilloscope tells all.