Sounds familiar, maybe I've heard a variant under another name.

Not many ABC implementations can deal with quadruple repeats like that - most of the code you'll see on the web that does it was uploaded by John Chambers, who has his own private software. Using the part notation avoids the need to do it, and makes it clearer what's going on. And I think you've added an extra bar in the second part by moving the start of the variant repeat - the fidder in the video you linked to does it as I have it below.

X:3
T:Rock All Our Babies To Sleep
R:waltz
M:3/4
L:1/8
P:AABB
K:D
P:A
FG|A2 B3  A|   G2 A2 G2|(F2  A,3 D)|F4
FG|F2 E2 F2|[1 G2 F2 G2| B4     A2 |F4:|\
            [2 G3  F E2| D6-       |D4||
P:B
FG|A2 f3  A|   B2 g4   | Af- fg fd |A4
cd|c2 E3  F|[1 G3  F G2| B4     A2 |F4:|\
            [2 G3  F E2| D6-       |D4|]

This is presumably from the Henry Reed collection in the American Memory archive at the Library of Congress. If it's like the other Reed stuff I've looked at there, there will be ten recordings of it, all different.