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 enough to roll through, the
dynamite red barrel must be standing at the door in the end. (If the red barrel were on its side at the door, it would necessarily be impossible to stand it up on the outside, because it was tipped on its side while it was standing somewhere inside the warehouse.) The path of the dynamite red barrel must therefore be something along the lines of this:
Now then, the first order of business is going to be
"move the doubly-open barrel two steps to the right".
To see why this must be so, consider the same puzzle with everything removed but these three barrels:
There are a couple of different ways of solving this simplified version, but in every solution the twice-open barrel has to move two steps to the right.
Now, in theory, it's possible to sneak the red barrel to the right, under the doubly open one, but that requires quite a shuffle, so we'll try to bring the red barrel up first, and to the right only after that, so we'll be following the path in the earlier diagram.
In the real puzzle, there's quite a lot of clutter in the way. Let's start by naming the barrels, and clearing up some space. We can always undo the cleanup later, if it turned out to be a mistake.
1. A-right 6. H-right 11. P-right 16. N-up
2. C-up 7. J-up 12. G-down
3. C-left 8. N-left 13. G-right
4. D-left 9. N-up 14. G-down
5. D-up 10. P-right 15. J-left
All this brings us to the following position, where we finally have the room to move the I-barrel:
It looks like we'll run in trouble, since the J-barrel is blocking the red barrel's path, and there's a lot of stuff in the top left corner, where we wanted to manoeuvre the red barrel. Turns out, neither of these problems is insurmountable, mainly because we got lucky with the exact way we packed away the top left barrels:
... 21. RED-up 26. RED-right 31. F-down 36. D-down
17. I-right 22. F-up 27. RED-up 32. C-down 37. RED-left
18. I-right 23. RED-left 28. RED-up 33. D-left 38. C-up
19. RED-right 24. J-down 29. F-Down 34. RED-up 39. D-down
20. RED-up 25. J-down 30. F-right 35. C-right 40. RED-down
And then it's just a matter of dodging the remaining barrels on the way (and they said donkey kong skills wouldn't ever be useful anywhere else):
41. RED-right 46. N-down 51. B-left 56. RED-left 61. E-left 66. H-up
42. RED-right 47. A-down 52. B-down 57. E-left 62. E-left
43. RED-up 48. A-left 53. B-left 58. E-up 63. E-up
44. N-left 49. A-left 54. B-down 59. E-right 64. H-left
45. N-left 50. A-left 55. RED-down 60. E-down 65. H-up
..and the coast is clear!
... 71. RED-up
67. RED-right 72. RED-right
EDIT: Praise be to @ManyPinkHats for producing this animation of the sequence: