The cross court strategy is winning me 75% of my matches at the 4.5 level, so it definitely is a viable strategy at higher levels. I am a pretty fit guy which helps I guess, as hitting those types of shots is tiring.
You are right about mixing it up and your also right that a good BH DTL is a game changer, but unless the DTL is a really good one, you will be in trouble because its pretty easy to redirect it CC and put you on the run.
Vil has a good point about fitness too, I agree
In the end, its whatever works for YOU really