Gallwood, This could sound patronizing, and it sure is not intended that way, but this is one of those things where you just gotta keep practicing. One day, you'll think you've got it mastered, and then you are at the beginning of having it mastered. You will benefit yourself with a bit of qualified taildragger training. Whomever trains you on one of those will be on you every moment to keep your heading and lateral position on the runway under perfect control.
Practice keeping your alignment to the extended runway centerline perfect from a way back, and yes, you don't stop flying, until the plane is not moving anymore. With the exception of low level mechanical turbulence, otherwise winds do not intensify as you descend. If you can keep it aligned with the runway on final, you should be able to keep it straight on the runway. Don't let it get away from you, and you won't have to get it back!
Like many pilots here, I have landed in crosswinds which exceeded the demonstrated crosswind capability of the type, in many types. My personal record is 37 gust to 43 knots 30 degrees off the runway heading in a Cessna 150, then 20 gusting to 26 knots direct crosswind, in a highly modified Cessna Caravan, with a large external load - during flight testing for that load. I'm sure that many Caravan pilots have exceeded that.
Fly the plane, don't let it fly you. The control is there for you to use, so make it work for you!