Can I safely clean the intake ports while the cam carrier is off the engine?

Yes, as long as the cams are off the valves will be shut, you can do that or even blast with walnut shell

Better pour some carb/throttle cleaner while engine is working. That is for intake manifold. If you want to clean inside of your engine, the areas where oil circulates, then again better to do it when engine is back online. There are carbon cleaner that is poured into oil system that circulates together with oil and cleans the carbon inside the engine internal, including inside the cylinders. It smokes alot while that happens. I mean when engine works. I havent done that in my own car yet, because I manually cleaned it off when removed the engine head. But for you removing the engine head right now is not an option.

Of course you change the oil and oil filter after that process.