Got it to work, but it is not my mod that is failing to move Space Exploration's new science packs to the correct tab, it is Science Cost Tweaker. I would say that you should go to Science Cost Tweaker's bug report page and ask for support for Space Exploration, but I am not sure how supportive of this they would be.
As for the tech loop issue, Science Cost Tweaker author has already said, "that's issue of SE-SPACE + BOBS , author of SE-SPACE made some stupid changes in research tree, that results in cyclic research with bobs plates." I believe the root cause is that Space Exploration Postprocess adds space science and material science to tungsten processing to gate the heat shielding tech, so maybe request on Space Exploration's mod page to remove space science from Tungsten Processing so that their mod plays well with Science Cost Tweaker.
Overall, I don't think it should be my mod that resolves these issues, it should be the other mods that resolve their issues.