We improved our Manipulate support some time ago, but you may or may not have tried your example recently. You can now interact with Graphics and Graphics3D within Manipulate.
You can now rotate the 3D plot in this example:
CloudDeploy[Manipulate[Plot3D[Sin[x y+a],{x,0,3},{y,0,3}],{a,0,1}]]
As well as select and resize the plot in this example:
CloudDeploy[Manipulate[Plot[Sin[x (1 + a x)], {x, 0, 6}], {a, 0, 2}]]
