Yes, it's done with intent, not by pushing under them.
Bingo. This isn't about moving uke. It's about moving yourself. And the only person keeping you from moving - is you.
Part of the problem is that people have way too much invested in the idea that there's this big strong guy grabbing on to their arm, and they've got to deal with the strong guy and move that strong guy.
That strong guy exists only as you create him. And the more you create him, the more your arm/s becomes an extension of him. That fires up your primal brain and then - even though you've gotta keep it cool - you're still having to do tricky jitsu leverage and throw in some muscle to move him.
I've got 120 lb women who can sit in seiza and have four strong guys put their eight hands on one of her arms and grab tight. I tell the women, "Those guys don't exist. You're just hanging out by yourself and you want to turn your hand over to see if it's clean." The four strong guys all topple over on each other. Works every time. I've got little kids who can do that like it's a piece of cake.
If you can create some big guy grabbing you - with your mind. Then you can uncreate them - with your mind. Seriously, there is no spoon.