Here you can see comparison of original (left) and new backlight (center). The new backlight is slightly brighter than the original; you can use larger resistors (270 or 330R instead of 220R) to lower the brightness.

I also experimented with general-purpose VLMW11R2S2-5K8L-08 omidirectional LEDs. You can see the result on the station on the right - the display is rather dim and there is significant backlight bleed on its right edge, where the LEDs are located. Thus I recommend to use only directional, right-angle LEDs like LTW-108DCG-HS10.

Since new LEDs need lower current to achieve similar light output, they should outlast the soldering station. This "trick" is generally applicable; high-brightness LEDs always generate more light at 2 mA than ordinary LEDs at 20 mA. At the same time, they consume less power, generate less heat and last much longer.