I realize this is an old post but am offering you some information anyway in case your still researching William Corum. I'm researching the Champ/Champe line and believe your William is the one found in Maryland with William Champ. Don't know if this would be much help to you but maybe will give you something to go on:
Found in the Maryland Calendar of Wills, Wills from 1635 (Ealiest Probate) to 1685 pages 82-95
Parker, Quinton, Baltimore Co., 16th Jan., 1674; 7th May, 1675. To Margaret Penry, James Smith, and Eliz: Harris, personalty. To dau. Eliza: Parker at 13 yrs of age, all real estate. Ex. Wm Slade. Test: Anthony Henderick, Henry Williams, Wm. Corum.
I'm finding that the Harris' are connected in with Champe's. I have another Corum in the area at the time also but would have to dig in my files to locate his name, believe it to be Robert. Hope this helps.