I have a condition whereby it takes me a lot of time to pass urine to where I can reach to a point that I am confident nothing will come out while I am praying. This takes a minimum of around 45 minutes up to two hours, with the average being an hour and ten minutes.

Because of this I have stopped praying my Fajr on time as it is too difficult to wake up an hour before prayer to use the washroom and even Zuhr/Asr because I can’t get that much time off my work schedule. As a result most of the times nowadays these prayers become qadha because even when I return home I spend upto 2 hours in the washroom, at which point it is nearly time for magrhib….
What is my obligation is in this case? Do I spend a normal amount of time cleaning myself and pray knowing that drops of urine might or will be released, or do I spend the extra amount of time to ensure that during my prayer I will be clean?…

You may also have OCD. Please see a therapist. There is nothing with that as well

In your case you should ignore the time and pray. Salah must never be missed. There is no excuse. So please ignore the time and the feeling of urine dropping and perform your prayers