Running super bright IR LEDs at 38khz off PN2222

dlloyd:

And how is that going to help, another 6mA of collector current?

Well, I've seen this problem before, ...................

I can't see anything in that explanation that would account for it being a fix for anything. I find the terms turn off and rise time confusing in the open collector context.
Even if your explanation were true then according to you the LEDs would be on for too long ( slow turn off ) but as the OP says they look dimmer not brighter. They would look brighter if the turn off were to be too slow not dimmer.