Using DynamicModule with EventHandler in the Cloud

Question

I am trying to write a nice little program to help me and colleagues draw outlines of objects in images

I came up with the following code which allowed me to click and hold down the primary mouse button to draw a shape:

imgs = {ConstantImage[0, {500, 500}], ConstantImage[0, {500, 500}]};

DynamicModule[{outlines = {{{}}, {{}}}, i = {1, 1}, n = 1, tmp, 
  labelimgs = imgs},
 EventHandler[
  Dynamic@
   Show[labelimgs[[n]], 
    Graphics[{Magenta, Opacity[.5], Polygon /@ outlines[[n]], White, 
      Line@outlines[[n, i[[n]]]]}], ImageSize -> Large],
  {
   {"MouseDragged", 
     1} :> (AppendTo[outlines[[n, i[[n]]]], 
       MousePosition["Graphics"]];),
   {"MouseUp", 1} :>
    If[Length@outlines[[n, i[[n]]]] > 1,
     AppendTo[outlines[[n, i[[n]]]], outlines[[n, i[[n]], 1]]];
     AppendTo[outlines[[n]], {}];
     i[[n]]++],
   "RightArrowKeyDown" :> If[n < Length@labelimgs, (n++;)],
   "LeftArrowKeyDown" :> If[n > 1, (n--;)]
   }]]

This works good enough in a notebook. Next I tried to evaluate the cell in a public cloud notebook (colleagues do not have Mathematica installed) which was unusable because every Dynamic step seems to be sent to the cloud and back.

Am I doing something wrong or is the cloud not intended to be used like this?