Harding still wins, but not as big as in real life. However, Wilson is handily defeated:
Senator Warren G. Harding/Governor Calvin Coolidge - 345 EV. 54.3%
President Woodrow Wilson/Governor James M. Cox - 186 EV. 43.5%
Interesting map; assuming your scenario, it sounds about right. But why the anomaly in Washington state?
I gave this state to Wilson because Harding carried it by a relatively close margin in real life. However, might be that he would have beaten Wilson in that state. The margin of victory is, however, still comfortable for the republican ticket.
Harding while only getting 56% of the vote carried Washington by a huge margin, due to the fact that the other candidates (Wilson and Christiansen) split the vote nearly evenly in the state (with a little left over for Debs). Wilson didn't even get a quarter of the vote.
I suspect that Wilson would do even worse than Cox. Cox at least had the record as a successful governor, while Wilson's presidency was not seen as successful at this point.
I think the map looks more like this:
