Hmmm... I've never actually heard of either of those. Well... I think I've heard of Music Tree ONCE. I'll have to look at those further! Thanks for the suggestions!
Anyone else? 
Definitely do look into them. Maybe I'm weird, but I love exploring all the different methods out there... and analyzing them... and experimenting with them... ...
As for supplements, I would purchase the bulletin from the Federation of Music Clubs. I use that to supplement in my own studio. Their lowest level is Pre-Primary, though that's for students who've had about a year or so of lessons. These pieces revolve around middle c and c position. Only a few have no position or are in different positions. Look Who's Visiting My Garden by Poe (I believe) is a great collection of pieces that has the student moving all over the piano.
Hal Leornard's showcase solos also work. Level 1\Early Elementary is a step below the Pre-Primary pieces. And it has a bigger font.
I would also supplement with the Faber Series - pretime, playtime ect. The pre-time levels are easier than the Level 1 HL. So for a student with about six months of learning, this would work. These pieces also revolve around middle C, but are short. No more than sixteen measures with bigger font.
And the last thing, would be the pre-notation pieces from Hal Leonard.
A lot of methods do indicate supplemental pieces. Double check the table of contents or online resources. I'm pretty sure alfred indicated supplemental pieces. Though, I'm not sure about the others.
If you're really at a loss you could just say where a student is in a particular book, or what skills they have accomplished, and we could recommend something for them.