If you can't sync up four DMGs together, you wired something incorrectly.

If you don't have 4 DMGs you can still test out all the ports individually to make sure they all work as long as you have 2 DMGs.

I can't try with 4 gameboys because i only have 2 flash carts, but following the exact instructions on Low-Gain's Flickr, i tested with 2 gameboys and LSDJ, and changed the cable to all 3 plugs of the DMG-07, and all of them worked.
https://instagram.com/p/2dpwjuhdwg/?taken-by=thanerd that's my final result.

I don't have proper tools either for removing the chip, and one of the resistors (between the chip and the wires blue connectors). I did what suggested Low Gain in the comments: add loads of solder around all of the chip's connector and trying to push the legs trough the holes. Then, i used a vacuum pump to take out as much solder as I could so that the legs basically were no longer surrounded by solder. Then i used a tiny flat screwdiver to pull the legs out. So i did that with all legs on one side, and for the other side, i tiled back and forth the chip about ten times until the legs eventually broke.

Last step was to repeat the "add way too much solder/vacuum pump" for each leg.

As a final cleanup process, i heated each pad from a side of the circuit board, and used vacuum pump from the opposite side.

Now i have to say that i'm all but a pro at soldering... But i like to waste hours ripping components off dead electronics... how funny it is to spend 20 minutes recycling a 0.01€ resistor from a 200€ item that could be eventually repaired :-)

So! With Low-Gain's fabulous directions, I have modded Nintendo's official 4-player adapter so that it syncs LSDJ. But apparently it's only good for connecting 3 DMGs in the end, not 4.
I've talked to a buddy and he's had this happen to him too.

Has anybody successfully modified the adapter to work with all 4 Game Boys? Did I just make some slight mistake while soldering?

*(also, WTB: does anyone have any modded adapters they'd be willing to sell? I don't own the proper tools for removing that stupid chip in the middle of the board)