Graphviz - Vertical order of leaf nodes - graphviz

Question

I'm trying to generate a Tree graph (left to right one), to illustrate an object reference tree.
Beside this, I want the leafs to appear vertically consequent, because this indicates some order of execution.
The dot code is as follows:
digraph G {
rankdir=LR
subgraph cluster_0 {
L1 L2 L3 L4 L5 L6
L10 L20 L30 L40 L50 L60
{ rank=same;
L1 -> L2 -> L3 -> L4 -> L5 -> L6 ->
L10 -> L20 -> L30 -> L40 -> L50 -> L60
}
}
subgraph cluster_1 {
R
D10 D11
D20 D21 D22 D23
D30 D31 D32 D33 D34 D35 D36 D37
}
R->D10
R->D11
D10 -> D20
D10 -> D21
D11 -> D22
D11 -> D23
D20 -> D30
D20 -> D31
D21 -> D32
D21 -> D33
D22 -> D34
D22 -> D35
D23 -> D36
D23 -> D37
D30 -> L1
D20 -> L2
D31 -> L3
D32 -> L4
D21 -> L5
D33 -> L6
D34 -> L10
D22 -> L20
D35 -> L30
D36 -> L40
D23 -> L50
D37 -> L60
}
What I've got far (using https://dreampuf.github.io/GraphvizOnline/ to render SVG):
The problem is, I want the leafs to show up in the order of declaration.
Following some posts on SO, I've been playing around with constraint / invisible edges / ranking system
but couldn't quite get my hands on it.
It'd be nice if some graphvizard could extend their hand over here.
note that this procedure will be later automated with python, so some robust idea will be more than appreciated.
note 2, the tree could have up to hundreds of leafs.
note 3, if you know some good python lib to generate Graphs which is more intuitive (for you at least) than Graphviz, please comment. I'm currently using pydot & graphviz (py3)

Answer 1

By moving the leaf nodes out and adding weights to them I have the following:
I changed the dot input to:
digraph G {
rankdir=LR
subgraph cluster_0 {
L1 L2 L3 L4 L5 L6
L10 L20 L30 L40 L50 L60
}
subgraph cluster_1 {
R
D10 D11
D20 D21 D22 D23
D30 D31 D32 D33 D34 D35 D36 D37
}
R->D10
R->D11
D10 -> D20
D10 -> D21
D11 -> D22
D11 -> D23
D20 -> D30
D20 -> D31
D21 -> D32
D21 -> D33
D22 -> D34
D22 -> D35
D23 -> D36
D23 -> D37
D30 -> L1
D20 -> L2
D31 -> L3
D32 -> L4
D21 -> L5
D33 -> L6
D34 -> L10
D22 -> L20
D35 -> L30
D36 -> L40
D23 -> L50
D37 -> L60
{ rank=same;
L1-> L2 [style=invis, weight=1000]
L2-> L3 [style=invis, weight=1100]
L3-> L4 [style=invis, weight=1200]
L4-> L5 [style=invis, weight=1300]
L5-> L6 [style=invis, weight=1400]
L6-> L10 [style=invis, weight=1500]
L10-> L20 [style=invis, weight=1600]
L20-> L30 [style=invis, weight=1700]
L30-> L40 [style=invis, weight=1800]
L40-> L50 [style=invis, weight=1900]
L50-> L60 [style=invis, weight=2000]
}
}