Because it is 6v6, it also means that Medic and co. will have higher awareness of who is around and who is not.
The best moment for you to spy is during the final uber push where all of them are focusing on DM and not aware of their surroundings. Do what you can do the best e.g Dropping a uber or killing their demoman before their final push etc.
Spy is indeed a utility and not supposed to be played 24/7 for the whole match, because why? fear and paranoia will eventually build up in the enemy's team and you won't be able to succeed any stabs. What a spy can do is to weaken the enemy's defense and give them a fear of your presence that allows your team to push with higher chance. I would only recommend to switch to Spy twice in 6's matches, but don't deem on your failure if you encounter any failstabs etc.
It is much much easier to play Spy in Highlander than PUG's, the best you can do is to understand the enemy's mind and play accordingly.
Hope you succeed
-AvEngErZx
P.S. Trickstabs are usually more prudent, so try to sneak around and make sure they buy your disguise at start. Kill the medic/demo and run (Remember to report to your team). If it fails, just shoot them with your ambassador xD