You can grab some barn doors for the LED fixtures if you get something like Opti RGBs or Opti Tri Pars. Beam shapers will give some of that control, but not like shutters or barn doors will. Maybe a dealer in your area or someone who has some fixtures can demo say a DW250 or any light with a beam shaper for you to show you what exactly the beam shaper does. It might give you the control you need. Can't hurt to look.
Cheapest fixture with shutters would be a Revolution. Personally however, I would much rather have VL1000s. While having modules for the Revolution is nice, everyone I have ever seen has had shuttering and rotating gobo wheel. Now if they had a CMY module, that would even things out a bit more. The VL1000 has CMY, frost filter, 6 rotating gobos, greater zoom range (super angle is 70 degrees), and a brighter lamp (7,400 peak lumens for Revolution vs 10,000 for VL1000 T or 15,000 for arc standard life, 14,000 for arc long life). You can also get the VL1000 T with or without internal dimmer, which means its dimmer curve matches the rest of your fixtures in your dimming system. All that for not much more then the Revolution after buying the modules. The biggest seller for me though is the CMY. Just food for thought if looking to go that route.