The good news is that you are a relatively mild case, seeing as you can use cubicles reliably - not much comfort to you I know, but it does mean you dont have too far to go.
You say "as long as no-one is watching". What evidence do you have that anyone is watching? I challenge you, in the nicest possible way, to find such evidence (this is what a clinical psychologist would ask you to do).
If they are looking, who has a problem? Not you, except that you are in a dodgy toilet.
Peeing for a "normal" guys is a totally forgettable, unremarkable event. They do not remember where or when they have been. It follows (and this is based on evidence) that they are totally not interested in another bloke's peeing. Not interested meaning not even considering looking. What is on their mind is what they were doing/thinking before they walked in, or what they are going to do when they walk out.
One of our trustees stood not peeing for 20 minutes to see what would happen. What happened? Zilch. He gave up out of sheer boredom.
So find some spacious quiet toilets with dividers between the urinals. Wear a coat that can hang either side of you. Give yourself time to calm down after the initial spike of apprehension - give yourself permission to wait say 30 secs before peeing.
As for attending a weekend, you have nothing to lose and everything to gain. Read the feedback on this forum.
And email me so i can put you on the list for notification