Lighting – use another brand of LED driver with IKEA lighting

Wow! You can use the screw in type LED bulbs, which contain their own controllers. These are typically dimmable down to about 20% using standard wiring. Here, we have Cree bulbs that look VERY similar to old Edison (tungsten) A19 bulbs, rather than the funny looking futuristic LED's. They're also much cheaper than the older screw-in LED's, about $8 each for the newest type. I don't know if they're available in your area. I LOVE THESE BULBS. ref: homedepot.com/p/Cree-40W-Equivalent-Soft-White-2700K-A19-Dimmable-LED-Light-Bulb-with-4Flow-Filament-Design-BA19-04527OMF-12DE26-3U100/205597080

If you're going with low voltage, (12V) you can use the LED strips and get rather creative, rather than using standard lighting fixtures. I replace fluorescent tube lighting with LED quite often now, for instance, or you can use them in an area with a diffuser panel below, as is typical in kitchens here. Friend of mine did the same with his bathrooms. I've also seen them used inside a paper light globe, wound in creative spirals and such, to make a unique decorative touch. Also consider using the strips as they were originally created to be used, as under-cabinet lighting. Be aware, however, you can't have a dimmer on the AC voltage side (before the transformer) and will have to use dimmers supplied for the 12V LED strips. I've seen these with remotes, and that's probably your only option for those. On a side note, the LED strips come in various color outputs (Bright white, Red/Green/Blue (for accent lighting or novelty lighting,) Warm white, etc.) The multicolor ones do require the specialty 12V controller to get all the effects.

Minimum Code Requirement and the Problem with Uneven Lighting

It seems like you're trying to correct for what is likely minimum code requirement wiring. Usually that means a single electrical box for a light fixture in the middle of a room, or a switched outlet ostensibly for floor lamps. The problem with this minimal number of fixtures is twofold:

1. As you identified, there are entire parts of the room that will be in a shadow because light travels in a straight line. You'll get some reflections off of the walls and other objects in the room, but that will generally be at a loss on the order of 10x.

2. The intensity of light from a fixture that falls on an object is roughly proportionate to the inverse cube of the distance from the light. This means that an object 9 feet from the fixture has approximately 1/27 the light falling on it as does an object 3 feet from the fixture.

The above two problems can be summarized as uneven lighting. The trouble with uneven lighting is that your eye will adjust to some sort of average of the brightness. The single bright light in the middle of the room is probably way brighter than that average, so it becomes uncomfortably bright to have in your field of vision. At the other extreme, the shadows are likely much dimmer than average, so your eyes will likely just see dark.

Both of the above problems are lessened by increasing the number of light fixtures.

How Many Fixtures Do You Really Need? Experiment!

To achieve even lighting, you need way more fixtures than minimum code requirement. My last renovation included one light fixture for every 25 square feet on average which represents about 5 times the number of fixtures that were originally installed. That's just about what is minimally necessary if you want to avoid both shadows and having bright bulbs within your line of vision.

Of course, the ideal number of fixtures depends on your room shape, light fixture design, wall, ceiling, and floor colors and material, and a bunch of other things. Accordingly, I found that it is best to experiment with your space before electrical rough-in by mocking up the fixtures and trying them out in the location to make sure you're happy with the result. For the experiments to be meaningful, you really need to have multiple fixtures so that you can evaluate how their lighting adds in the room. During renovations, I usually just screw a bunch of fixtures on cords to the original walls and ceiling drywall and see what happens. If you're trying to preserve your finishes, you'll need to get more creative -- I've used tripods and photography light stands before too.