A single CD4041 gives you 8 strong outputs (≈10mA each) - 4 of each polarity. Connect all the inputs (pins 3, 6, 10, 13) to the 555 output. The 555 and 4041 can be powered from the same voltage source, anywhere between 5 and 12V12V*. Add a 1uF ceramic capacitor between 4041's power pins 7 and 14. Pins 1, 4, 8, 11 provide "positive" (non-inverted) outputs, while pins 2, 5, 9, 12 provide inverted outputs.
For this application, the 4041 is hard to beat probably.
There's no need for series output resistors after the 4041 outputs.
I found this PRL-414B diagram online and have been wondering if it could be even simpler.
That is a circuit made for a specific application - not at all what you need. You can do it all with a single chip, whether it is a CMOS digital buffer like the 4041, or a quad op-amp - either CMOS or LM2902/324.
* NE555 and CD4041 will work together up to 15V, but there's no switching speed benefit to that. So unless you really need the high output swing, 12V is a very reasonable option.