Honestly, I wasn’t to happy about the idea of changing the style of my barrel, but I always try to follow advice, or at least give it a try and see how it looks, even it sounds like a bad idea…
Woke up in the middle of the night with an idea on how to approach this and just had to try it out to see if that would work!
This is what I did:
‘Alt D’-ed my four planks and scaled and rotated them like so:

Also added those planes to form the rings.
Added an Empty at the middle of the ‘front’ left edge of the leftmost plank and parented everything to that Empty.
Then added two Simple Deform modifiers like this:

(CTRL_Barrel is said Empty)
The Deform Angles of the second Modifier are slightly different for each plank and 360° for the rings.
Gave the rings a Solidify Modifier.
The result was this:

Now I just had to move the Empty to place the barrel in the scene:

Still need to ‘fix’ the rings, add ‘rivets’ to them and make a hole for the ‘plug’, Make some final adjustments if necessary. But first I’ll try and finish my sleep:)