OldSteve:
The receivers are tuned to only detect IR at 38kHz, and to reject continuous IR. In a remote control, a 38kHz carrier is used, then that's modulated, (quickly turned on and off), to generate an output that is pulsed according to the digital bits that are being sent. Then, because you want to drive the IR LEDs with a current of 100mA, you need to use a suitable driver for each, a transistor, MOSFET or multi-channel driver chips like ULN2003, ULN2803 etc.The next point is that the IR LEDs are wide-angle and not a tight beam, so moving your finger towards a given key will not necessarily be recognisable as that key. You could consider laser rather than IR LEDs maybe, if it weren't for the point I mentioned earlier - even if you did get that aspect working, how does your system differentiate a valid keypress from a finger just above the key?
I'm afraid that under the circumstances, you have the exact opposite situation. It's not possible with the equipment that you have.
I do have access to a ULN chip. I'm not yet sure of the exact model, but it is something close to the ULN2003/ULN2002.
I believe I can remedy the angle problem one way or another.