Going back to the original image, which road are you saying is being crossed by moving from N5 to M7
Yes, I think it's the Q7-P6-O7-N6 road.
this reminds me a lot of this Q&A which is why I still think no Road is crossed, but keeping my mind open.
I agree with that Q&A, you can't Dash from the G7 Rubble, through G8, to F8 or H8.
A4.63 never says "cross a road" (probably to avoid the inevitable "why did the 10-3 cross the road" jokes). It does say from somewhere "on one side of the road" to somewhere "on the other side of the road" but it never defines what that means.
For instance, in your RB map example, what if the end of the road in G8 hooked slightly NE, coming close to G8/H7 but without touching the hexside (see 33AA2)? If a hook counts, how much of a hook? What if it were a bulge, like 20DD8? Is that enough to allow Dashing from CC9 through DD8 to EE9. What about 33Q8 and R8->Q8->P7?
Maybe we could get Perry, Klas, every ASL Rule Lawyer, and a few devil's advocates to all sit down for an hour or two and work out a rule wording. For now, how does this work?
Any Road Location has roads crossing (a) one, (b) two, or (c) ≥ three hexsides.
(a) If only one hexside is crossed by a road, assume the road continues and crosses the directly opposite hexside, and handle it as case (b).
(c) If ≥ three hexsides are crossed by a road, the moving player may pick one, and treat it per case (a), or any two, and treat it per case (b).
(b) Exactly two hexsides are crossed by a road*. Call them hexsides A and B. You can start at hexside A and go either clockwise or counterclockwise to get to hexside B. Let Set 1 be those hexsides encountered going clockwise from hexside A to hexside B; let Set 2 be those hexsides encountered going counterclockwise from hexside A to hexside B. Hexsides A and B are members of neither set. A unit can Dash if it crosses one hexside in each Set.
* Either two actual roads, or one actual road and an assumed crossing from (a), or two actual roads and ≥ one road being ignore from (c).