I meant to get back to you on the reading lights but been too busy. If you look at your photo you will see the two LED chips, under the lenses, and the driver circuits on each side. Those driver circuits are delivering a set current to each LED. To increase the light output you would need to replace both the drivers and the LEDs. First keep in mind that the LEDs are creating heat, and anything brighter may need a heat sink included; also, they would need to be mounted in the same location as they are lined up on the fresnel lenses (so height should matter too). It might be possible to bump up the output of the existing drivers; otherwise a new driver circuit is needed for each LED.
If you look closely the driver circuits each have a controller that has a single IC (3 legs on one side, one large leg on other), 3 diodes, and a single resistor. If you are lucky the resistor or diodes will determine the IC's current output, so could be replaced to change up the output. To solve that problem first you need to know what the IC is, which is written on the top. Get that info and download the datasheet and you can decode the driver, and work out what would be needed to change the output. I must warn you that replacing those tiny surface mount chips is difficult, but possible with the right tools. Otherwise you would have to hack into the circuit at the right place and install a small driver board. Keep in mind there are two ways of turning on the lights: manual switches on the board, and remote computer control.
Replacing the LED chips may be the easiest part of the problem - or not. First, don't let the size fool you: even very small LEDs can be quite bright. IIRC a 5mm square LED can have 1000 lumens or more, which is a lot more than this application can safely use. The real issue is heating, and dissipating that heat. I have a small, stainless steel, pocket light that puts out about 500 lumens on high; it gets too hot to hold in about a minute (LED flashlights use the metal cases, or at least the metal heads, for heat dissipation). In this case your LEDs are mounted on a PCB, which is an insulator, although there may have been some copper plating added to help conduct heat away. You will need to keep the LED to a small output, and probably need a heat sink as well. Of course the driver output needs to be less than the max for the LED, and the LED heat output needs to conducted away by a large enough heat sink.
Places like fasttech.com that serve the flashlight enthusiast community (flashaholics - I'm serious) will have the LEDs and drivers.
Personally I think you should learn to live with what you've got. If you are getting on in years then you might be getting cataracts if night vision is an issue. But if you are determined then get me the part number of the IC and I'll take a look.