Look at what I found at FOM:
1) Polynomial Shift Sequences http://www.cs.nyu.edu/pipermail/fom/2003-June/006781.html Theorem 3 provides an e0-recursive function that >* all f_a(n) for a<e0
2) Diophantine Shift Sequences http://www.cs.nyu.edu/pipermail/fom/2003-June/006772.html Same here, again an e0-recursive thing (see theorem 3)
3) Degenerative cloning http://www.cs.nyu.edu/pipermail/fom/2001-May/004892.html Read Theorem 4. Cool stuff there, he even named the function himself and gives bounds
4) Another independance result for PA http://www.cs.nyu.edu/pipermail/fom/2000-October/004463.html Because we nether have enough e0-recursive functions, Theorem 2 presents us a new one :v
5) Finite linear games // Limited memory games http://www.cs.nyu.edu/pipermail/fom/2009-August/014002.html Hehe, an extension of Promise Games that leads to MORE functions that crush SMAh =3 See Theorems A2.2, A5.2, B2.2, B3.2, and B5.2 - they ALL leads to extremely fast-growing functions!!
EDIT: I'll search for more!! C: