Would higher tension strings help?

This is a question I probably should have thought of a while back.

I have a small problem with one of my ukes. It is beautiful, has a wonderful sound, the whole package. But there is one problem. When I play it, especially the first string, I can easily move the strings as I am fingering them, sometimes pushing them over the edge of the fret board if I am sloppy.

I know I can work on my technique, and I am, but it just hit me that maybe if I got higher tension strings, there would be more resistance to this movement and it would not happen as much.

Is that a possibility? If so, do you all have any recommendations for higher tension strings? Linear, if that makes a difference, although I usually use a Fremont blackline or another type for my low G.

Thanks in advance.

That would work, to a degree.

(I believe SouthCoast have a range of tensions.)

Sometimes when I was lowering down strings, they became too floppy to be useful, (i.e. when I tried DGBE on a soprano).

I use concert low G fluorocarbon strings, (Living Water in my case), on my tenor scale ukes, & I dont have any tendency to push them off the edge, but I do sometimes get unintentional pull offs, but that's down to me.

Also, what is the action like?