So I have an almost complete solution in which I am reasonably confident about my solve steps, but I end in an impossible state...
I am hoping someone can correct this because I know I am E/W or L/R dyslexic but I have gone over it too many times now! :)
purple corner squares have no choice, because they lie on exact opposite pairs.
orange squares follow directly on from purple as given.
blue needs 1W + 2N total, with one pair in two options.
green needs 2S + 0E/W total, also with one pair in two options.
if we choose the final yellow square as SE, we can't go NE twice in the central squares; therefore it is SW.
the two middle yellows are therefore NW and NE, and the red column tells us the order.
this gives us the blue boxes for free.
and the left over green squares must be W and NW, with the order is also fixed by yellow.
purple squares are a total of 2S and 2E in 3 squares, therefore S, E and SE
but the red row cannot contain S, so the top is E (and a free orange box!)
also the blue row can't contain SE, so the bottom is S (giving us some pencil marks for the rest)
lastly, the yellow column needs 2E and 1S, which can only be added in one order.
orange column can be resolved because we can't have a 2nd SE in the second bottom row.
this gives us the blue column for free.
the remaining boxes in the red row need to mirror the placed ones, so: N, NW, and W
but we know the green column can't contain W, giving us the column as well.
yellow follows for free, and disambiguates the rest of the red row.
purple column must contain 2S and 2E (ie S, E and SE) but red row can't contain a S.
yellow column must contain E and SE as well.
given we know we will have a SE in the blue row, we can't have 2 Es to complete it so we can choose both yellow and purple orders.
this solves blue, which solves green which solves orange... bottom half complete!
the purple column requires 2S and 2E, and only 1 combo in 4 boxes: S, E, SE, O
also, the red row can't contain S or E which fixes the O and solves the red row.
the blue row can't have any more S, so we now know where the E is in the purple column.
blue has a N and a NW left, and the yellow column chooses the order giving us the yellow and green squares.
Slightly tricky, but there are only a few combos to get 1S in the purple column.
Using the red row, I note that I need to use all 3 N options to get my target, and what is left over needs to be E-W balanced (so can only be E and W!)
This means that the only thing that can go in the purple/red intersection is E, solving purple.
The blue row can only be NE and E... but NE can't be in the yellow column because I know the red row has no O in it.
This now solves yellow, green, and red can be selected from the only two N options available.
[EDIT] Started solve again from this point, as puzzle up until now remains the same!
Step 8: Some limitations:
There are a few limitations we can add now. Only one square in the orange column can contain an E, meaning the red row has only two options: [W | S] or [SW | x]
Yellow can't support anymore E, so the orange/yellow intersection is E-W neutral.
But purple still needs 2W in total, and so does the yellow row. So we have definite W-type arrows in the two remaining yellow squares.
And finally, this means the top green is E-W neutral as well.
Step 9: Uh-oh... But now, what..?
Unless I have gone crazy (again!) I don't have any further reason to eliminate options...
This would mean that there are (at least) 3 solutions which fit the clues...
Sorry - I think I may have broken it again..?