Lighting, Light Fixtures, Ceiling and Exhaust Fans - Converting Switched Outlets to "HOT"

I have series of outlets on a run where all of the top receptacles are switched (bottom receptacles are always hot). I want to convert the top receptacles to be hot as well. I found this diagram in another post and it is almost exactly what I have in place. The only difference is an additional red conductor at the switch, that controls an overhead light.

http://www.selfhelpandmore.com/switchoutlet/plughalfswitched/outlethalfsw.htm

(There is also another switch in the wall box that controls a ceiling fan only.)

The black conductor going to the overhead light/outlet switch is inserted into a push-in connection (top right) at the back of the switch. The red conductor for the overhead light is also inserted into a push-in connection (bottom right), while the red wire controlling the switched outlets is on a screw terminal (bottom right outside).

My question is this . . . Can I simply move the red wire going to the outlets, from the bottom screw terminal to the top screw terminal where the black wire is pushed in? That would mean the red wire was essentially connected to black. Could the red wire be taped black since it is running power? I want to make sure this doesn't violate code. Is there a better way to do this?

What you said will work electricly. I would take the two wires you suggested and twist them together then twist a pig tail. to them to attach to the switch.

I also would only use the binding screws on the switch. I do not like back stabs.

Don't use the pushing connections. They are known to go bad. Make all your connections with a wire nut.
You don't need to tape the red wire. Red is a hot wire color that does not need remarking.

I'll make the changes as you suggest - thanks for the help guys!