Just how are you intending to use the backhoe...digging the hole ...or pounding them in.
I have a 4 in 1 CX300 loader on my 3320 tractor and have installed 280 post 4 to 6 " in wet weather and in middle of summer's worest heat and dry season.
I pound them in with the back edge of my bucket - using about 4" blows.
Now I'm a pile driving crane operator and have the timing down very good.
I was told it can't be done this way and yet, like I say 280 post mostly 5" or better and there all in 2ft or better,these are 8foot post's.
One thing - once there in ,leave them alone for a day or so to set ,before you add boards etc to the post.
If your backhoe bucket can reach the top of the post try it! One won't hurt anything.
I have a friend hold it till I get the bucket on it he keeps it straight one way and I eyeball it the other ... I set the bucket on the top ,press down till it won't go any more and then jerk the lever to allow the bucket to come up about 4 to 6 " and slam back into the top of the post.
Try it you might like it!
But that's just me.