How can I make up for prayers I performed incorrectly or with nullifiers, or omitted out of ignorance, to clear my conscience and reassure myself?

Many of the things you mentioned do not invalidate the prayer. For instance, the absence of khushu' (devotion/concentration) does not invalidate the prayer nor necessitate its repetition according to the majority of scholars. If there was impurity on your garment that you were unaware of, your prayer is valid. The takbirat al-intiqal (transitional takbirs) are a sunnah (definition) according to the majority, so a prayer is not invalidated by someone who omits them. Wiping over socks is sufficient according to the preponderant opinion. Washing the hands up to the elbows without re-washing the palms is sufficient according to some scholars. Rinsing the mouth (madmadah) in ablution is recommended according to the majority.

As for what you are certain you omitted regarding a condition or pillar of prayer, if you were ignorant of the ruling, you are not required to make up the prayer according to some scholars.

It is permissible for you to act upon a less preferred opinion when there is a need and to remove hardship.

If you wish to make up the prayers, calculate the prayers you are certain were invalid and make them up, while being cautious of waswas (whisperings/obsessive thoughts), ignoring them, and not giving in to them.