From what I've read, 0x80070005 is an access denied error. I'm still not exactly sure why this permission is required to update a list. I've gone through the list and group permission settings several times over, but nothing else stands out to me. The only other documented case I've seeing of this issue is from the following Stack Exchange discussion from 2011. Seems they were also having a similar permissions issue, but a resolution was never reached unfortunately. The user Adam B suggested enabling Use Remote Services, as you can see above, that's already added in my case, Contributors still must have Managed Lists enabled in order to update lists.
http://sharepoint.stackexchange.com/questions/15494/lists-asmx-updatelistitems-returns-unexpected-error-0x80070005
http://sharepoint.stackexchange.com/questions/15494/lists-asmx-updatelistitems-returns-unexpected-error-0x80070005