Is what the questioner does—delaying ritual purity due to obsessive doubts and excessive scrutiny, and the consequent missing of prayer—considered intentional neglect of prayer?

We have mentioned to you that you are sinful for what you did, whether by intentionally delaying prayer without an excuse, or by delaying it due to giving in to waswasah (whispers of Satan) until its time expires; that is not permissible. Muhammad Siddiq Khan al-Qinnawji described someone who gives in to waswasah until the prayer time expires as one of the disobedient, and that he becomes an abandoner of the prescribed duty. It is not permissible for you to sleep after the time for prayer has begun unless you know that you will wake up before the time expires, with enough time for purification and prayer. Furthermore, your repeating ablution six times and bathing for an hour and a half is a trick of Satan against you, and Allah has not obligated this upon you. So, fear Allah and desist from the ignorance you are in. It is stated in Ibn Hajar al-Haytami's Al-Fatawa al-Fiqhiyyah al-Kubra that waswasah only gains dominance over someone who is completely overwhelmed by ignorance and folly, and who loses their discernment.