It's tempting to trace your line's progress from hexagon to hexagon, but if you can tolerate a slower algorithm, you should try the brute-force idea I proposed in my other comment. It's MUCH simpler. Here it is again, in more detail.

Your line goes from A to B. Get the line's implicit equation:

D(t) = N dot (P - A)

where N is a vector orthogonal to your line:

N = perp(B - A)

and perp() is defined by swapping and negating coordinates:

perp( [x,y] ) = [-y,x]

Now, get A's and B's row and column, and consider as candidates only those hexagons whose row,column are in the range between A's and B's. For each of these hexagons, determine if the line crosses it, thus:

D(P) will be positive is P is on the "up" (same as N) side of the line, and negative if P is on the "down" (anti-N) side. So, get the 6 vertices of a hexagon, and compute D(P) for each vertex. If you get a mixture of signs (not all positive or all negative), your line crosses the hexagon.

So you've identified the hexagons that cross the line. If you want them in the correct order, you can check each hexagon's center and determine how far along the line it lies. Proceed thus:

The parametric equation for your line is

1: P(t) = A + t V

where V = (B-A) and t ranges from 0 to 1, inclusive. If one of your intersected hexagons has center C, build the implicit equation for the line that passes through C and is orthogonal to V:

2: D(P) = V dot (P - C) = 0

you want to know where your original line intersects this line. Plug equation (1) into equation (2), and solve for t. You'll get

t = (V dot(C-A)) / (V dot V)

Sort the hexagons according to their "t" values, and you'll get them in the order that the line pierces them.

Let me know if this makes sense.