I'm with 4zfed on the possibly intermittent loss of oil pressure. There is also a screen in the oil supply line of the CCT that can get clogged but I don't think problems there would cause the oil pressure light to come on.
It does sound like you have a real oil pressure issue although the readings you measured are well within spec.
To answer your question, I've never heard of a chain slipping a tooth on a 1.8t due to a bad CCT but it is probably possible. I've read about people who have had the chain loose enough to rattle against the valve cover or who have driven with no pads on the CCT but even then it usually didn't skip a tooth. I'm not saying it couldn't happen but it doesn't seem to be common.
The chain can definitely jump if the rub blocks have popped off.
You can compress the tensioner slowly with a bench vise or one of those vise grip quick clamps or a basic big c-clamp. I even squirt them down with oil before compressing them. After it is compressed you can install the holding tool to install it. They usually show up new with the holder tool installed though...The rub blocks are available separately also, and cheap too, but I have had a lot of those break when installing them.
Sometimes it's a lot easier to just take your cams out when you change the cam chain tensioner or replace rub blocks. This also allows you to see and reach deeper into the head to pick all those rub block bits out that can cause major issues later.
I was going to experiment with getting the rub blocks a little more flexy to get them to pop on easier by heating them up, but I never did. I was going to drop them into boiling water. The rub blocks are definitely a weak point because I have never seen them not break up in a high mile car. And on a V6 or a V8 they're usually quite the pain in the ass to change out.