Are you saying that your wife hasn't done a DNA test ?
If she has, bring up her matches list and select Search. Enter Woodger and search on that. If you get some matches, check to see if any of them have Wooding in their trees.
If not, clear the search and try with Wooding. Also, put her results on all the sites that have been mentioned on your other threads. Use 'Search Matches' on any matches that look possible to get groups - colour code these groups.
Also, have you used the 'search Members Trees' from Ancestry Search page. This might produce some descendants of Edward Wooding.
There's no quick way of a finding possible ancestor - lots of searching and using all of the tools that have been discussed, etc.