James - all you need to do is to just call the callback directly and ensure that you pass the correct inputs. Since your callback signature is
function movefront_Callback(hObject, eventdata, handles)
then you need to pass the handle to the movefront control (this is hObject), the event data (which can be empty as it seems to be only valid for key presses and other events like that) and the handles structure. So your key press callback can become
function figure1_WindowKeyPressFcn(hObject, eventdata, handles)
movefront_Callback(handles.movefront, , handles);
moveback_Callback(handles.moveback, , handles);
Try the above and see what happens!