Get a product called "GOOF OFF". stuff will remove the latex paint quickly and will not touch the original paint. Ive used this stuff and its great. get the liquid and not the spray can. you brush it on a section , wait a few minutes and remove with a putty knife. You will be surprised at how it lifts off the whole area. Keep a wet sponge or rag handy and wipe over the area , this helps pick up any of the stuff that got thru the latex,
good luck!