Here's my attempt (maybe I'll get graphical when I have the time, text only for now.)
First, label the non-dynamite barrels like this:
and develop a notation: <Barrel name>-<direction> means move the named barrel to the mentioned direction, by whichever means it can move there. (It will always be unique.)
Then, make the following moves:
Frédéric Servais has apparently done a lot of study of this problem, particularly his Masters' thesis, Finding hard initial configurations of Rush Hour with Binary Decision Diagrams. For the 6x6 case without 'trucks' (3x1 pieces), he finds a maximum of 65 steps (plus the final move of the red car out); for the "full" 6x6 case, the maximum he finds is 92 ...
OK, this one's going to be way more difficult than the ones before. The first observation is that an open barrel standing somewhere can only stand somewhere else if it has rolled in between, and rolling requires a two-space wide path. And the doubly open barrel of course cannot even stand at all. So, let's get rolling! (Hlyaaargh.)
Since the door isn't wide ...
First i'll start off by naming the boxes
The red box will be called R
I do the following operations
-> means tumble/roll right, whichever available
<- means tumble/roll left, whichever available
U means means tumble/roll up, whichever available
D means tumble/roll down, whichever available
It starts off with:-