Re: reducing a 4" crock to 11/2" for a launder tub drain.
First a floor drain should be going to a storm sewer not a waste sewer and you should not be running gray water into it.
Second if you seal it you have no floor drain and if you have water leak the water will just fill up your basement.
That being said the cause of your problem is the fact that it takes a certain amount of pressure to force the water Through the trap and it is easier for it to over flow because water takes the path of least resistance. You could take a piece of 4"PVC about 2ft long and silicon it into place to create a stand pipe. Then run your 1½" pipe into it. The dam created by the stand pipe will build enough pressure to cause the water to go down the drain rather than out on the floor.
Be sure you live your life, because you are a long time dead.-Scottish Proverb