Maybe I disappoint you, you mentioned that Russian allows very flexible word order. That is true, but at the same time some word orderings are more usual than others, so basically when Russians try to mimic Yoda speech they will try to get sentence in any unusual word ordering. This still will sound grammatically correct. I have seen some "instructions" - how to "speak Yoda" in Russian on the websites, they will give some rules, but in fact this is just the preference of a person who create the given rule set. The only rule that seems relevant to me is to make the sentence less usual ordered, but not too much, so that it still very easily understood.
Since the real purpose of Yoda speech is to make everybody happy and laughing, the rule is to break any rules every time.
I can share my own algorithm:
1) analyze your original sentence and remove the words that make it hard to reshuffle
2) pronounce any word and then analyze which word is logically would go after it
3) do not put that word after it, puzzle the audience, put any other word from the sentence, less expected in this position of a line
4) repeat puzzling as many times as possible, more times the flow is not going where the audience expected - more fun
5) in the end you must get the perfectly clear and understandable passage
The tricky part is to make as many "shifts" from normal wordflow but arrive in the end to a perfectly correct phrase, this is where people will start laughing - when they realize their ears struggled but they are happy in the end with a clear sentence.
My guess is that those "Shifts" that occur when you already hear some word and your mind expects the next word and suddenly you hear something unexpected, a verb instead of a noun, subject instead of an object etc - your mind goes nuts for a second, fantasies arose inside you and that's what makes you happy. And when the sentence come to an end, all is suddenly settled in a correct phrase it makes you laugh.
But the mind adapts quickly, that's why multiple Yoda phrases in a row are not funny. They are better served unexpected and one in a time.