Different fill orders in geom_bar per discrete x-value

I have this ggplot:

What I want to do is change the order of cat2 in each distinct cat1-category in decreasing order of share:

• For cat1 == Z: i would come first, because it has the largest share in that cat1, followed by k, then j etc.
• For cat1 == Y: j would come first, because it has the largest share in that cat1, followed by h, k, f, g
• and so on for all cat1-categories.

I know I can control the order by defining factor levels, but since I need a different order in different cat1-categories, I'm not sure how to do this.

Can someone enlighten me?

df <- structure(list(cat2 = c("i", "k", "j", "h", "g", "j", "h", "k", 
"f", "g", "j", "h", "k", "f", "g", "i", "k", "j", "h", "f"), 
    cat1 = c("Z", "Z", "Z", "Z", "Z", "Y", "Y", "Y", "Y", "Y", 
    "X", "X", "X", "X", "X", "W", "W", "W", "W", "W"), share = c(0.254318086442458, 
    0.217254586570476, 0.13303361614456, 0.107317457057957, 0.0796390207719751, 
    0.255762968963295, 0.198921069216629, 0.177295815678624, 
    0.100770340584133, 0.0971042138291394, 0.222007778896866, 
    0.177174367182501, 0.156891912894117, 0.097677432116308, 
    0.0975337223454565, 0.503295513011454, 0.154491050393999, 
    0.114284166914891, 0.0802892036069214, 0.0549053589320047
    ), pos = c(0.477447245936265, 0.108627293285238, 0.283771394642756, 
    0.658265017686473, 0.751743256601439, 0.305177300160272, 
    0.532519319250233, 0.088647907839312, 0.779469237979754, 
    0.680531960773118, 0.26789580234255, 0.467486875382234, 0.0784459564470585, 
    0.702446497377094, 0.604840920146212, 0.520422973814617, 
    0.0772455251969995, 0.211633133851444, 0.812215332123805, 
    0.879812613393268)), .Names = c("cat2", "cat1", "share", 
"pos"), class = "data.frame", row.names = c(NA, -20L))

library(ggplot2)
ggplot(df, aes(cat1, share)) + 
  geom_bar(stat = "identity", aes(fill = cat2)) + 
  geom_text(aes(label = cat2, y = pos)) +
  coord_flip()

Note: my current thinking is that perhaps it could be done using a new category with the levels set as 1st, 2nd, 3rd, 4th, 5th but if I use that for filling, different cat2-values for example i for Z and j for Y would have the same fill-color because they are 1st in the respective cat1-category which I wouldn't want.