I've found a program that does just that. Dual Display Mouse Manager slows down your pointer at the transition point between multiple monitors, as if you squirted some digital molasses along the edge of the screen.
You can use the program defaults, which work just fine, or you can tweak the delay (by default, 150 milliseconds). There's even a program setting to prohibit mouse movement to the other monitor unless you hold down the CTRL key, but I can't imagine a scenario in which that setting is convenient.
Dual Display Mouse Manager makes the shared edge between my monitors just "sticky" enough that I can easily hit the UI elements I was aiming for. A small convenience in a frustrating world.