You can get any number of configurations of AA battery holders. Mouser Electronics, an online electronics distributor has a whole page of them in their catalogue at AA Cell Holders Page from types that can accommodate 1 cell all the way up to 10 cells. Here are a few representative pictures of the ones available.
These are available with solder tabs, wire pigtails or snap fitting connections.
Not a complete answer, but here's some more info.
Brightness
While there are ways to calculate this that aren't that complicated, it requires knowing many coefficients that are not readily available, so ends up being an educated guess at best. You can do just as well totaling your current lighting's lumen output, then adjusting for changes in fixture styles. (I consider even a simple LED strip a "fixture" for the sake of this discussion) It's a starting point. If you use proper task lighting, there's a lot of room for variance in total levels.
Uneven light
You do not want to see the actual LED elements, it's really annoying. Besides diffusers, indirect lighting techniques work well, though require more lumens due to losses through reflection.
Positioning
I'm not sure what the issue is with parallel surfaces. The efficiency is mostly inherent in the fixture's ability to direct light where it's needed. The mounting surface has little to do with this, you need to direct the light where it's needed.
White Light
The "whiteness" is measured in degrees Kelvin. The temperature a black body must be heated to emit the same color of light. Standard daylight is often taken to be 6500K, anywhere in the 5000-7000 range is close enough for most tasks. You eyes adapt quickly to small variances. In residential settings, daylight is considered too harsh because we are so accustomed to incandescent lighting, so most home lighting is produced to output more in the 2000-3000K range to mimic the orange incandescent lighting.
Noise
How audible the noise is varies by manufacture and environment, as well as personal temperament. I don't think noise data is readily available. Testing in a noisy store will not yield any useful data, other than if you can hear it from a few feet away it is too loud. Noise can be attenuated by placing it in an enclosure, but keep in mind power supplies generate heat that has to be removed by ventilation, you cannot seal it into a sound proof box.
Try to place power supplies as far from your pillow as possible, trying to sleep is when it will be most bothersome. Placing it lower so there is likely to be more furnishings obstructing a direct path will help, as well as being surrounded by soft materials that do not reflect sound as well.
Best Answer
They make a lot of socket connectors and other kit for novices. Unfortunately this product is a bit too "out there" and I wouldn't expect to find stuff like that. You'll have to do it old-school, by soldering leads onto the solder pads.
Solder on short (<12", 6" is better) #20 or #22 wire pigtails, stranded if possible. Otherwise the wire is too stiff and it tends to "wag the dog" i.e. the wire pushes he strip around and can even tear the solder pads off. I know that wire seems awfully light but it's OK for a short pigtail as long as you keep current below absolute limits for that wire (under 5A for #20... or under 3.5A for #22...)
Those tie onto the feeder wires. At such short distances voltage drop won't be an issue.
What you really have there is 5 channels plus a "common". Now, 3-channel amplifiers are ubiquitous. 4-channel (RGBW) amplifiers can be had. 5-channel, forget it. You'll be forced to use two 3-channel amplifiers, which is fine. You don't need to distribute the amplifiers all over the place if you have a big enough central amplifier to drive the whole shebang and are willing to run 6 feeder wires. You'll want to make the common extra large; it's carrying 5x the current of the others...