LL(1) CFG for triple amount of b's compared to a's?
I believe that any string able to be represented by a CFG can also be parsed in LL or LR. That is just one of the features of CFG's. The grammar you have originally written can be parsed using LL as the upper-case $A$ will act always as your left-most variable to be expanded and simplified. 

I think your problem with constructing the grammar can be solved by also including rules in which the lower-case and upper-case $a$'s are switched, though, that is a rather clunky solution. 

$S \rightarrow A$ 

$A \rightarrow \epsilon | baAbb | bAabb | bbbaA | bbbAa | bbaAb | bbAab | aAbbb| Aabbb$