The textures of the toys by Joesemsims are repo'd to the Maxis urn, but that leads to weird recolors. What steps should I take to un-repo them, since those meshes already have a relevant recolor TXMT included?
And an optional question: how to stop making them floating? (I assume OMSPs didn't exist yet in 2006)

You need to add a txmt, mmat, txtr and relink those resources. The txmt included is for the shadow. To move the location of the mesh you need to use Milkshape or Blender to adjust. Or more easily, create a new clone. However, those toys are from the toy bin, I am pretty sure they exist as playable toys without the bin. You may be better off using WCIF instead.

@HugeLunatic I already imported the TXMT, MMAT and TXTR to the original mesh file, but the mesh is still repo'd to the Maxis urn. What step am I missing? (see attached screenshots)

The objects are downsized AFAIK, hence I want to try to make them work better.

If they don't have any recolors attached, the easiest way is to just extract the mesh and texture, then clone a new object with whatever properties you want the objects to have, and change the mesh and recolor, then re-use the GUID from the original object (unless you want to use both objects, then you have to give it a new GUID).

Most likely the floating issues are from the mesh itself. If so, you'll have to move the mesh where you want it in a meshing program (for a middle centering - center it X/Z and make sure the lowest part of the object is close to or at 0 but not in the minus for the Y-coordinate).

It would be easier to just adjust the height then repo them to the toybox, wouldn't it?

Change the GMDC Models Name to
toybox_woodpaint
Commit

Change the SHPE Subset Name to
toybox_woodpaint

and SHPE Materials Definition File to
toybox_woodpaint
Commit

Change the GMND tsDesignModeEnabled Items Name to
toybox_woodpaint

and tsMaterialsMeshName Name to
toybox_woodpaint
and String to
toyBox
Commit and Save

Start > Object Tools > Fix Integerity
Okay and Save

Skip the Fix Integrity after repository. It's not needed, and in any multi-state object it will rename things you don't want renamed.

@HugeLunatic - Thanks for the advice, I didn't know that.