It appears that you wish to produce a substantial amount of diffuse light with a controlled mix of color in an enclosed space. Bear in mind with each decision that any electricity you waste will go towards heat, so you should probably consider maximizing thermal performance and minimizing power wastage with each step. If the frame and mounting points really are 1/2" aluminum, a decent design likely will mean you don't need a fan, depending on ambient temperature, heat coming off the rest of the machine, etc.
I'm actually here on stack exchange to get more information to design a general purpose modular led driver system =).
I don't know how much space you have to work with in your machine, but one thing you may wish to consider is fewer, more powerful individual leds running at a lower percentage of their total capacity, and using a more effective diffusing lens than whatever is already present, like acrylic with microbeads or a multilens setup. Because these higher power LEDs can be purchased on or mounted to MCPCBs, this will help greatly with your thermal management. LEDs become more efficient at lower average current levels, lower instantaneous voltage levels and lower thermal levels. Also running LEDs at a lower portion of their total capacity will in many cases greatly extend their lifespan (see datasheet). Being modular, they can be easier to replace. That being said, the following will also apply to a large number of weaker LEDS.
You have a large number of matching LEDs all being controlled at once, so as others have mentioned, you have the advantage of being able to use a series set up to ensure the LEDs share current. You do need a different total voltage for each string of LEDs, but you can do things to mitigate this, like if you have 60 red LEDS, 60 green LEDS and 60 blue LEDS and the reds are 2.2v each and the greens are 3.3v and the blues are 3.2v, the voltage of 60 blue in series would be more than 180v, and say I didn't want to work with more than 50V, for the blues I would have to make a parallel set of at least 4 matching strings of 15 or less LEDS in series. If I wanted to go lower, I could go to 5 strings of 12 or 6 of 10. As long as you have four or five LEDs in series and you don't exceed thermal spec they will current share fairly well. If you make a list for each of your colors of the arrangements you can make and the voltages they require, you can choose voltages that are in relatively the same ballpark. This will eliminate many resistors, especially if you go so far as to actually use the LEDs in full series strings. using high power LEDS rather than a larger number of them can aid in this, provided you are using a powerful enough diffuser. Having IR LEDS calls for one more series or series/parallel bank of them.
The next thing to consider, in order to eliminate all of those nasty resistors, is to add voltage regulation. Because you have 4 banks of LEDs, you need to produce 4 voltages unless the voltages required by each bank are very very close to one another. LEDS function most efficiently at a constant voltage and if you PWM control them, they tend to operate at the efficiency they would if they were continuously on. So it is best not to overvoltage them, even with your pre-PWM voltage. This means that the voltage your PWM driver (arduino) is switching should ideally be pre-adjusted to be exactly enough (maybe 5% more) to power the LED bank at the maximum brightness you will want it to run at OR the minimum voltage the bank turns fully ON at, whichever is greater. It would also be wise to have your arduino current control the LEDs to prevent thermal runaway. This can be accomplished by having it monitor the voltage across a 1 or .1 or .01 ohm series resistor while in the ON part of the duty cycle. The resistor will not counter thermal runaway, but you can make your arduino reduce the duty cycle of the channel if the voltage across the resistor starts to rise, indicating the LEDs are heating too much and starting thermal runaway. In this way you use the Arduino's "intelligence" to regulate the LEDs, rather than using a resistor to regulate by burning off heat. In resistor regulation circuits you often waste ~1/2 of your total power, but that's assuming you don't already have thermal concerns. In an enclosed box, producing more than twice as much heat as you need to becomes a problem even after you get rid of any thermal runaway problems, decreasing the efficiency of the LEDs, causing them to produce more heat in order to maintain the same brightness, which in turn decreases efficiency further. The better your LEDs are cooled, the less you have to worry about this, but unless you want to modify your machine with a comically large heat sink, it's best to consider thermal problems at each step of the design, and then at the end, based on the necessary thermal load, add any heat sinks or fans that might be necessary. If you follow all of my advice here and have enough high power LEDs that you don't have to run them too hard, typically just the MCPCB that these LEDS come mounted to will be adequate to cool them at considerable brightness levels. If you overvoltage them in your pre-pwm voltage, they'll heat up more as I mentioned, so avoid that.
I'd figure out what LEDs were in the existing plan, figure out what their total output would be, and then find matching color high power LEDs mounted to MCPCBs, say CREE XP-G2 or G3, or Nichia, whatever, such that at their minimum rated turn-on voltage(most efficient) they would produce that amount of light plus 200% for error(you can usually run them substantially below that voltage for further efficiency improvements. This could be surprisingly few LEDS, so if necessary I would increase the number further in order to decrease the amount of diffusion necessary. I would then use a spreadsheet and figure out what the best series/parallel bank arrangement for the LEDs would be to get their voltages within a reasonable range and or closer together if they aren't already. I would then make or purchase one variable voltage or current regulator for each of the four(or more) channels, and use the Arduino to switch that. You may wish to consider a Buckpuck or similar switching driver. Next I would turn on and adjust all four channels so they barely fully turned on, and whichever was brightest of them, adjust each of the other voltage sources up so that in the ON state, they produce an equal amount of light. Let the Arduino control the PWM drive on the LEDs running off that supply. Start by adjusting the arduino duty cycle down to find the brightness of light actually required, and have the duty cycle regulator consider that to be 100% for the purpose of the rest of my programs. If necessary, I would increase this brightness, the number of LEDs, and or the effectiveness of the diffuser as necessary to eliminate any hotspots or unwanted artifacts.