silly fat cats (or) fat silly cats
Silly fat cats is more euphonious. Both are grammatically correct.
'Fat cats' idiomatically means rich people, or rich powerful people. So it could be that you are calling those rich people silly, as opposed to calling those silly cats plump.
funny fat cats (or) fat funny cats
The rhythm of these phrases is about the same, so either.
funny big fat cats (or) big fat funny cats
Big fat funny cats rolls off the tongue. It has much better cadence. So definitely big fat funny cats.
funny really big fat cats, or really big fat funny cats
Again, the cadence is the deciding factor - really big fat funny cats.
really in this situation means "very", and modifies the adjective which immediately follows, so you are right to move the adjective "big" along with it...
Compare
A really expensive black leather handbag/purse.
This bag is black, as well as being very expensive.
An expensive really black leather handbag/purse.
This bag is expensive, as well as being very black.
You are correct that the first three sentences are grammatically valid.
You are correct that the fourth sentence is incorrect. As @Sander states, the copular verbs glue the rest of the sentences together, all but that final them. This leaves the them referring to something that isn't actually there, and thus is said to be dangling.
With respect to which roll naturally off of the tongue, you're correct that both #1 and #3 do; I've heard both forms in casual conversation.
Best Answer
Although normally called an "adverb", probably is often used to modify an entire sentence - in which case it normally appears at the beginning (or the end, if it's "parenthetically" added after a comma)...
In other contexts, syntactically it's more like an adjective than an adverb, in that it normally modifies the immediately following term...
Both of these imply that you will have moved by then (possibly to the north, but most likely to the south).
Implies that you will move to the south (possibly much later, but most likely "by then").