Hello there!
I agree, this looks like a root/pelvis misalignment. When you are implementing the auto rig, you should get a prompt like the one below, regarding the height difference between your models, so please make sure the offset is applied, or modify the bones to have the same height.
Since running without “Run IK Rig” improves the animation, but makes the character movement not cover the same distance, that means IK is most like working in the first place, but since the root/pelvis is not properly setup, the animation plays wrong. Make sure the alignment is correct, then test setting translation mode to Absolute, which should help with the incorrect distance move.
There are other methods to test for scenarios like this. Checking around the community, there’s a video guide covering usual problems with retargeting, as well as a similar thread with further solutions. Also, it always helps to revisit UE’s docs on the subject matter.