The 6N138 was designed to drive large loads even with a very low LED current (1 TTL unit load = 1.6 mA). The high CTR makes it rather slow; the MIDI specification says that you can use it with "appropriate changes".
With a single pull-up resistor, the output transistor switches off very slowly because it cannot go easily out of saturation, and reducing the load resistor not only increases power consumption, but also does not improve the timing enough so that it would be reliable for MIDI in all circumstances.
One method to improve timing is to add a base bypass resistor (RBE) between pins 7 and 5. It both speeds up switching off and slows down switching on the output transistor, so you have to use a value that balances both to reduce the pulse width distortion:
(source: HP's Optoelectronics Application Manual)
So with IF = 5 mA, you can use a pull-up resistor RL = 1 kΩ or 2.2 kΩ, and end up with RBE = 10 kΩ.
An even better method that avoids balancing issues would be to clamp the output transistor with a Schottky diode:
Use any small Schottky diode with a low capacitance, e.g., SD101, BAS70, RB751.
In any case, MIDI ports are idle most of the time, so the pull-up resistor's current probably does not matter that much.
A high-speed optocoupler with a push/pull CMOS output would eliminate the pull-up resistor, but would also have a non-zero power consumption when idle, so it would be likely to be worse overall.