Hi T.--
Show him whispering, and different quiet, silly voices. He'll still scream sometimes. :)
Clinginess means he feels more secure when he's right with you. Do you have a baby carrier/sling, like a front or backpack? That might help, so you can have your hands free while still carrying him. I don't think you need to "break him" of anything. Babies are sort of wired to feel better when they're closer to their moms--more so at certain ages than others. Rocking to sleep is a kind thing for you to do, and doing it again in the middle of the night is too. Tiring, and kind. :)
Have you ever heard the expression "a need fulfilled is a need extinguished"? What I'm getting at is, the more you pull away from his clinginess, the more he'll seek to cling to you---denying a need doesn't make it go away. (Unless mom always says no or doesn't come, and baby gives trying to get her to come help, but I think that's a very sad alternative.)
I remember some days I felt my back would break from the baby clinging to me, and that I would lose my mind from not sleeping, but it didn't and I didn't. And I feel proud that I can look back on having done a lot of kind things for my daughter at that age, many of them in the middle of the night. :-) I'm sorry to hear that your husband is away so much, that can't be easy.