Have you looked at Outlaw's manual for the 886? I don't know what to do with the Tivo to have it output video without scaling and deinterlacing it (my cable box can do this in theory, but in practice the firmware is so clunky, hard to use, and unreliable that it's almost not worth the effort). As for the 886, though, you will want to do a few things: (page numbers refer to Outlaw's guide).
Page 18: go into the "Input/Output Assign" menu, "Monitor Out" sub-menu, and set the "Resolution" to "Source." This will let you set the resolution separately for each input.
Page 22-23: Go into the "Source Setup" menu for each input (Tivo and BDP-83), select the "Picture Adjust" menu, and set the "Resolution" setting for each. The BDP-83 will want to be set to "Through" and the Tivo will want to be set to either "Auto" or a specific resolution that best matches your display's native resolution (I use 1080p in my case, but it depends on your display). You will probably end up using the same resolution here that you are using for the BDP-83.