Is it permissible for me to disregard drops of urine that may come out after urinating, and suffice with performing ablution and prayer without waiting or checking for their exit, in order to get rid of the waswas (whispers of the devil/obsessive thoughts) and suffering I am experiencing, knowing that this could lead to complete recovery from this incontinence within a short period?

What you are experiencing is merely a whisper from Satan (waswasah), and we advise you to disregard it. Perform ablution immediately after relieving yourself and do not pay attention to the whispers of Satan. The fundamental principle is that nothing of urine has exited unless you have certain, absolute conviction that you could swear by. Ignore these whispers and deal with urine naturally, for that will cure you, Allah willing.