See that’s the part you aren’t getting.
Your base skeleton is wrong which is what is causing the baseline jssue.
You need to fix that first.
Once you do that, things are going to start looking much better in the first place.
Then, you can worry about any additional fine tuning.
And yes, if you export an animation you can create a pose off the frame and use the created pose to fine tune the retargeting a bit by matching poses…
Its kind of similar, importing the pose vs fixing the skeleton - but fixing the skeleton is always the better option.
The closer they match (bone rotation values) the less issues you will get.
Oh and btw, the bone roll on your fingers is wrong if they distort the way you have pictured.
Each bone has axis to it. The chain of the fingers needs to be oriented identically.
In blender its trivial. Select the bones, select the last one with the right roll, and set all rolls to match the active bone.
In 3ds max there are similar things.
Same for copying a pose. Usually ita frame based.