Trying to simulate FPS style mouse control

Google is failing me.

Basically I’ve made a shooting gallery, with a scope.

mcRange is the unzoomed target range.
mcZoom is the zoomed version of the range that appears in the scope.
mcScope is the scope, the crosshairs are at 0,0.

All 3 clips sit on the stage. The scope’s position is fixed, and I move the targets based on mouse input. mcZoom is under a mask layer which contains a copy of mcScope.

prevX is the last recorded stage.mouseX
prevY is the last recorded stage.mouseY

sensitivity is just what it looks like.

here is the relevant code

addEventListener(Event.ENTER_FRAME, scopeHdlr)
stage.addEventListener(MouseEvent.MOUSE_MOVE, moveHdlr)
var prevX:Number = stage.mouseX
var prevY:Number = stage.mouseY
var sensitivity:int = 10

function scopeHdlr(e:Event):void{
    mcZoom.x = mcScope.x - (mcScope.x - mcRange.x)*mcZoom.scaleX
    mcZoom.y = mcScope.y - (mcScope.y - mcRange.y)*mcZoom.scaleY
}

function moveHdlr(e:MouseEvent):void{
    mcRange.x += (prevX - e.stageX)/sensitivity
    mcRange.y += (prevY - e.stageY)/sensitivity
    prevX = e.stageX
    prevY = e.stageY
}

This all works flawlessly, except when the user moves the mouse all the way to the extents, they cannot pick it up and recenter it like one would in an first-person style shooter.

I would prefer not to use a joystick style system where if the mouse is to the left, we slide the targets to the right until it returns to the dead zone. Is there a way to either:

Capture mouse input outside the stage (99% sure we can’t) or

[TL;DR short cut]

Can I reset the mouse position via actionscript. This would be ideal, while an “aim” state is active I could just recenter the mouse every frame, and shift the targets based on mouse delta.