Ok. Thank you for posting this level of detail. It will drastically reduce the back and forth guesswork and allow for a more concise illustration.
Simplified illustration
Here is an animation that shows what is happening. The yellow model are two objects inside an assembly. The second two are the same objects as independent models. You can see how they behave differently when using the (M)ove command one tries to pick up one vs the other. In the yellow example, because the cylinder is part of an assembly, the lowest object(cube) in that assembly acts as an anchor to the build plate. In the green model, the cylinder just falls to the plate.

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What you appear to be experiencing is that you are caught between the automated function upon import of importing as a group versus independent objects. As you’ve seen firsthand, neither yes or no option works well if you want to get more granular control.
So the method I suspected you may not be employing, assemblies, is the better method to achieve what you described.
There are many other methods but this is probably the easiest to explain in a forum post. If this does not work, please let me know why and we can try another approach.
To restate what I believe your objective is, you want the rivers to lay on top of the topographic maps. If I misunderstand that, please correct me.
The first thing we have to do is repair any non-manifold objects. Look for the error symbol

This happens when the 3D mesh does not convert cleanly leaving holes in the model. This will break a print in unpredictable manner. Do not be surprised if this takes several minutes of computing time to fix.
Separating the models.
If I understand you correctly, you want to essentially create two interlocking “puzzle” pieces that will print separately and then snap together after print. For this you want a consistent bottom layer height. Your current options are interfering with that.
TL;DR – This is the briefest way I can explain one approach.
There are probably five or six different ways to achieve this. As stated above, I believe this option is the easiest to explain.
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Clone the model.(CTRL-K)
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Delete the parts of the model in each clone assembly which are not wanted thus isolating the mating land mass and river system to each puzzle piece. So 004 becomes one assembly and 005 another.
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This will create this problem. The two pieces are now at different heights:
Note: Color changed for illustration purposes only to provide contrast.
Since this is now part of an assembly, you can independently move the elevation using the (M)ove tool.
While I admit that this method is tricky and it requires some ninja mouse skills, it is the most straight-forward way to manipulate the model. Make friends with the CTRL-Z hotkey(undo), this will become your best friend during trial and error(CTRL-Y is redo if you change your mind).
An alternative, if the mouse movements are too tricky or god-forbid you’re a glutton for punishment and are attempting this on a a MAC with trackpad😉, you can use move tool and dial-in the layer heights manually. Painful? Yes, but an alternative to the mouse.

Here is the completed exercise file. I’ve never used this site so good luck and use at your own risk, there may be tons of tracking cookies but your file is too large to upload here. (37MB)