Ok, one thing is that latency is situational so can depend if you are tired, stressed, and what mood you are in. Latency is the time between standing at the urinal and actually starting to pee.
For someone without paruresis it normally takes 7-14 seconds to start peeing but any latency is normal so can be affected by any of the above things and also lack of urgency as you've already discovered.
If misfires begin to affect you then your mate can tell you to say this to yourself before you try to pee "What if i can pee" instead of "What if i have a misfire again". CAN is a more positive word than MISFIRE so your brain will recognise that and react accordingly in time.
How about you and your mate saying out loud (but quietly) to each other "What if i can go". If your mate can go after saying it then it will encourage you to do so too.
Ask your mate to stand near you at a urinal when you don't need to pee. This is called faking. You stand at the urinal for about the same time as you would if you were peeing but you intentionally don't pee. This helps you get used to the urinal environment and used to standing there doing nothing. When you then have a misfire in the future it will bother you less because it will just feel like you are faking again.
If you are unable to pee during a visit to a urinal you can walk out, stay in the area (or go on to the next public toilets), take a deep breath for 4 seconds and then breath out. Repeat the process until you feel relaxed, a greater level of urgency, and ready to try again and then go to the urinal in your own time. Don't rush these things until you are as comfortable as possible.
A tight abdomen (stomach) can make you think you are ready to go when your level of urgency isn't yet high enough.
Lastly, i suggest you and your buddy do what's called anchoring. This is where you do something as a symbol of self-praise for having a success.
How about you and your mate giving a high five to each other before you go into the toilets and on the way out.
This represents that you WILL have a success and that you DID have a success.
I hope you can understand my English and am pleased to read you are making an excellent start.