Wow, took me 4 weeks to finally find time and gradually work on those 4 items, huh... I really need to find more time for this :D

Anyways. I did get everything in order, and took your comments into account, so let's go over the changes.
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Y-Axis Motor Mounting:
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For a long time, the only place i saw to mount the motor without it interfering with anything was below the base. This would have been achieved by lengthening the side part below the linear bearings/ballscrew. Luckily, after taking a step back and looking at the model again, I found a much better place to do so, right next to the Ballscrew for the Y-Axis itself. The spot there is pretty much perfect, since it is below any part of the Z-Axis' top part, even if the Z-Axis motor is mounted on the back, but at the same time, it is above the lowest part of the Z-Axis, meaning it does not add any constraints for the workspace inside the machine. I would plan to get those mounting plates(the green ones) cut from steel sheets, since I can get that rather cheap.

Z-Axis Motor Mounting:
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The second picture carries a lot of annotations, but I will go into the important parts again: I found two possible mounting spots for the Z-Axis motor, both are shown. Following your advice, I went for a NEMA 23 Motor on the Z-Axis, instead of a NEMA 34, like I am using for both the X- and Y-Axis. I now have the option of mounting the motor on the back, possibly compensating some of the torque the spindle places on the Y-Axis carriage. This, however, means that I need one more part to assemble the carriage, since I cannot just take two bent sheet metal parts. I would also need quite a significant amount more material, as you can see. The mounting on the back of the plate carrying the Z-Axis Bearings, would simply be using unused space that would already be there, and it would be relatively center on the axis, but possibly add to the torque of the spindle, since it is a bit forward. Using slots in the mounting bracket, I could easily change the height of the motor in that position to fit the mounting point needed, however.

I am unsure what spot to choose here. The top mounting position has quite a couple things going for it, but the back position does offer torque compensation at the price of significantly more complicated carriage assembly...

X-Axis Motor Mounting:
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The X-Axis mounting was easy to do, since I already had a good talk with one of the mechanical engineers in my workplace about that one. It is a simple Omega Belt Drive structure, driving both ballscrews from the same motor, just as you advised me to do. The two pulleys on the movable arms are tensioned using springs, not only to tension the belt, but also to increase the contact area of belt on both the ballscrew- and motor-pulleys.

Finally: The Back bearing mounting plates:
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These are basically the same as on the front and just simple metal pieces to hold the bearings of the ballscrews. The problem I currently have with them, however, is this: They are three-dimensional 20mm plates with pockets milled out of them. A better idea I had, to make them easier to manufacture, was to instead buy some longer Ali extrusion in the X-Direction, to bring the front and back edge of the machine more in line with the front face of the ballscrew-mounting-blocks, both in the front and back. Then I could use simple flat sheets of metal with some shimming underneath to equalize any tolerances. This would make those mounting brackets easier to manufacture, but add some "dead-length", when it comes to the ali extrusion, where it becomes longer, but the rails or axis are not. Still, I think that would be a better approach.
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To-Do:
Normally I would now lay-out what was on my mind, when it comes to next steps, but I cannot come up with anything concerning the CAD model, it looks pretty much done to me. What I need to now look into, however, is the electronics side of things: Find out what I still need in terms of controllers, motors, Power delivery, etc. and get some rough pricing, as well as model it into the CAD as needed. Where would be a good way to start here? For the gantry and machine design there were some helpful collection threads on here, comparing different gantry designs, for example. Is there also something like this when it comes to the electronics?

As always, thanks for any help!
-Chrono