can you cool manicotti noodles off completly before stuffing
What is your method for cooling the pasta? Is the goal to have it cool enough to work with? Or to stop the cooking process, keeping in mind it's going in the oven later?

My opinion is that the only cases when you should rinse pasta after cooking is if you're making a cold pasta salad, or if you're going to serve it plain. The reason why you should avoid this method of cooling it in virtually every other case is because in a great majority of the time you'll be adding a sauce to your pasta and you want the starch that's covering the surface of the pasta to help the sauce stick. This way all of the ingredients in your dish will be well incorporated and just give it that little nudge that makes all the difference.

Ultimately if you end up with overcooked pasta out of the oven you can always reduce the cooking time in the pot and if your sauce has enough moisture the pasta will keep cooking through in the oven (which would most likely be the cause of your problem in the first place, but we're clever, we'll work around it, take advantage of that!!).