Yes, you can use cream cheese but as mentioned, you'll have to 'doctor' it to give it the same properties of marscapone. Marscapone is a 'sweet' cheese so make the adjustments to bring the taste the same... some sugar and as suggested, maybe some milk to get the consistency right.
I also have a mean tiramisu recipe from a good chef friend in Perugia, Italy.
In working his recipe, which is close to yours with one exception, I found that beating the whites very, very stiff helps when the flavors all come together to make the cream less runny. My exception, there is whipped cream in it as well and that must also be whipped firm, almost to the edge of butter, to keep it stiff.
Also, the secret ingredient is to add about 2 teaspoons of the ground espresso coffee to the cream. After it sits, the flavors come to life and the coffee, as it is so finely ground, is not an issue when eating.