I'm not sure all thoughts are neutral since meaning comes from thoughts, not just feelings. What is the meaning of the word 'poop'? There is no emotion needed to know what the meaning we commonly give that word.
The feelings, when fully listened to are a signal from the essence within us that mechanically manifests and holds life in it's place - so they have the capacity to provide far more than just a colouration of meaning. In the context of judgement though, the feelings reveal the gaps in the logic that are always present in judgements.

The process I use was channelled 'from god in the first person' in a fairly recent [series of books](http://www.rightuseofwill.com/books). While I cannot confirm everything that is written in these books and some of what is written will be WAY too challenging for many readers - I CAN confirm a large amount of the contents from lived experience and have healed my spine using the wisdom passed through there.

The method given for judgement release is to verbalise into vibration the counter phrase to the judgement - including also compassionate self acceptance - along the lines of:
"I forgive myself for believing for so long that I am stupid and I release the judgement that I am stupid".
Since we typically hold hundreds of thousands of judgements, this might seem a bit clunky, but it has a vibrational affect that reaches deeper than is possible when only operating in thought.